Ooh, that's a lot of restrictions!

I think bingo or telepathy (if students secretly choose a word/sentence instead of writing) might work with those restrictions. The Ninja Game might work well, too, since it's basically just Battleships with the whole class involved. Taylerwithane has a lot of ppt games that can probably be modified to fit your needs- her game thread is over here:  https://waygook.org/index.php?topic=121225.

Good luck!

4 different games per class is ridiculous...
I also suggest bingo and telepathy plus class connect 4, Pirate game played  in team rows (usually the first person of a row asks a question, the next answers. Then switch to the next kids in the row after that turn), reading bomb games, noonchi game, different voice reading, catch the sentences, sparkle game, last one standing game, team (row) roleplay reading, decoding games, worksheet unscramble, word searches, find the sentences in the book, play games that are usually team choosing games like find the star but have the first student choose one and then the group repeats and then the class repeats, and I'm sure there is more but they're not coming to mind.  I recommend a lot of listening and repeating.

Here is my version of a 'whole class' bingo game.
Have a bingo board on the screen/board.

1) Students choose 1 sentence and write it down.
2) S1 reads their sentence and the teacher crosses out on the board.
3) S1 chooses the next student to read their sentence.
4) Continue until the someone reads a sentence that is already crossed out.
5) The game is over. Start a new round – new slide or repeat the same slide but students must write a different sentence from round 1.
6) The class wins if they get a one-line bingo.
OR continue the game to find out how many bingos you can get.

(Or you could use a word document on the screen and use a highlighter to show which sentences have been said.  If you use that option you could make the game more 'interesting' but deleting the highlight if a second student says the same sentence.)

Sorry - I've just looked and realized that the game has students writing.  Maybe they could draw a picture? or if they have a set of flashcards each they could secretly choose one.  Or you could number each sentence/word and they just write down the number.  You could use pictures then too.

Did you see the eslintherok website - some good ppt games here - and they can be personalized to whatever vocabulary you want. (no pictures though).  The disadvantage is that you cannot download the games and must be played on the computer you created the vocabulary list on.  [My co-teacher had the idea of screen saving - but this is still quite a bit of work.  However the games give some ideas.]

Guessing game
This is one of my favorite and little preparation required.  One set of flashcards for the teacher. 
1) Teacher secretly chooses a card and asks the relevant question (eg 'What color is it?' 'What did you do yesterday?' ...)
2) Students take turns guessing by using the key sentence structure (eg 'It's red'. 'I visited my grandma.' ...)

I know you can't have team games but you can award team points (divide the class into two groups?)

No/little writing

Also, another poster had a lot of good ideas but I thought maybe you'd like having the actual ppts to look at. You'd have to edit them of course, but it could give you a jumping off point :)

Not much speaking, but have you tried plickers? https://get.plickers.com/ You print out QR codes for students and they hold up the cards to answer. (depending on the direction it'll register as A, B,C, or D) You scan them with your smartphone. I did this at the high school level and played it as a golden bell/ last man standing style quiz.  (Each card has a number so you can register it to the students' names)

What about a battle ships game in partner (two students can turn their desk opposite of each other (while keep their plastic walls up around their desks) and they can take turns asking and answering questions while trying to kill off each others battle ships? I did battleships with my 2nd and 3rd grade middle school students and it seemed to work well!
Also, wow four game per class!!!! Is your co-teacher serious?? I find it hard to get through 2 games per class !!! I think you should sit down with you teacher and ask if you can do 2 ~ 3 games, where one can be a sentence of word unscramble (the whole class looks at a scrambled sentence and they each student tried to unscramble it within 30 second), those who are successful can raise the hands and say it out loud (speaking practice), and the rest of the class can repeat after you show them the answer, followed by a bingo type game, and a battleship type game??

Yeah, I need to talk to her about this more. 10 mins per game is the rule she seemed to want enforce the most. I'm not quite halfway through the amount she wants me to prep for the first week, and this level is not sustainable. If she is adamant about keeping it like this, I'd likely need her to prep stuff as my other lessons will be neglected.
And thanks for the suggestions. :D

Yeah, I'm afraid I don't have any suggestions that haven't already been mentioned.

This KT's expectations are unreasonable, imo, and I would be the type to tell her so (albeit as professionally as possible). It really isn't sustainable at all, and there's no point to it. Really, there is no point, there's a lot of wasted time in there, lol.

If I come across some other ideas I'll drop them here, but yeah... let us know how this all plays out, haha.

Cheers, I did give her the expectation of a lot of trial and error while I figure out what she is okay with, and what the students enjoy. If I wasn't already prepared for all my other classes for the next few weeks, I likely wouldn't be able to achieve that for this week. Especially since I need different content for each grade. I'll likely talk to her about it after classes this week, and try come up with something more reasonable. I'd even compromise to 4 activities, if 1 could be a small writing / listening one haha (cause I can bang out a lot of decent ones, as I do them at my other schools). However, she also did say, that if the amount of prep is too much, to let her know and she will ease up.
She gave me some really crazy restrictions on the games though haha. I'm worried the students might not enjoy them this week cause I'm trying to cater to those restrictions. >.<

Yeah, there is no educational or pedagogical justification for these constraints, its just a capricious useless set of stricture.  I would ask for the educational reasoning here.

I'm not sure this is the educational reasoning, but she mentioned the previous foreign teacher was extremely strict with the students which, made them hate the class and in turn, made them not study/practice. With me, she wants my stuff to be fun, to help get the students to practice and stuff again. My guess, is she worries that if the stuff is over 10 mins, the students will lose focus, or something. I don't see her until tomorrow, so I'll talk to her about it then, and try work it out with her.

Here is another game/activity that I used yesterday.  I have used it for elementary students grades 3-6 and it seemed to work well with them all.
5-8 flashcards seems to be a good number (with elementary it is pictures with words, but can be sentences or phrases etc)

I call it the 'snowball game' as the snowball get's bigger and then disappears (melts away).

Put up flashcards one at a time and students say the activity while doing the actions.
Eg. Can I come in? Sure.
Can I come in?  Can I play it?  Sure.
Can I come in?  Can I play it? Can I sit here? Sure.
Can I come in?  Can I play it? Can I sit here? Can I use it? Sure.


When all cards are up, take them down one at a time from the beginning and students say all the cards by memory .  This time say ‘Sorry, you can’t.

Can I come in?  Can I play it? Can I sit here? Can I use it? Sorry, you can’t
(Can I come in - by memory)  Can I play it? Can I sit here? Can I use it? Sorry, you can’t
(Can I come in? Can I play it - by memory) Can I sit here. Can I use it? Sorry, you can’t
… … …  Can I use it? Sorry, you can’t.

OR – Randomly take them down until all cards are down and students can say them all by memory.

Awesome, cheers for that, I'll add it to my list. I've been making a list of games to try out, with a rough examples of the rules, to see what my co-teacher / students will go for if they don't like what I've prepared for tomorrow. :D

Here is the edited 'Whole Class bingo' powerpoint file

You can change the text easily by just typing in what you want on the coloured tiles.
Then drag the coloured tile and retype the words below (or you could just leave it blank).
Just be careful NOT to swap the coloured tiles around!

Cheers for this. :)

After classes yesterday, the teacher was really happy with what I prepared - I easily broke her 10 mins per game rule because the students were really into the games I prepared.
Though, the big game where I thought a lot of the learning would happen, ended up being slightly too difficult around the 30 - 40% mark. So, the teacher has asked me to keep my warm up game, and change from games to maybe a short story with a lot of questions after, and maybe finish with another smaller game at the end. To kind of balance fun and learning, as we didn't really do learning part yesterday haha.