Not really sure what you are trying to say but ...

Looking at your profile page you have no cards that can give you the free card drops.

Card drops are not unlimited. Each game has a set amount of free drops. After those drop you need to buy or trade with people for the ramining cards needed to craft the games badge.

All you need to know about Steam Trading cards but where afraid to Google for.
http://psteamcommunity.yuanyoumao.com/tradingcards/faq/

IM does not actually run any game exe file. The game does not even need to be downloaded for IM to work.

So having AI War running was not an error from IM.

I know drop rates are affected one one account when you play/idle multiple games but never heard of it affecting two different accounts on two different pc's running from same IP.

http://psteamcommunity.yuanyoumao.com/groups/idlemastery/discussions/0/620700961011240417/

Then you most likely got the cards for those games.

Go to your badge page. It will tell you there what games still have card drops. Any game with drops will have a green PLAY button. If there are no games there with card drops then they are all gone.

Yes running two games at a time slows the drop rates. It essentially takes the same amount of time to get the cards when you idle two games together as it would if you ran them one right after the other. There is no real benefit to doing it.

It is not suggested to run IM while running a VAC game.

While no one has been know to be banned for using IM while playing on a VAC server is it really worth it for virtual trading cards to take that chance?

The reason has been answered plenty of times here in this discussion group.

http://psteamcommunity.yuanyoumao.com/tradingcards/faq
Give it a read it should explain things ..

A quick summary;
1) Free cards from idling / playing are not unlimited.
2) Not all games participate in the Trading Card program.
3) The amount of free cards from idling / playing games is approx. half of the cards required to craft the badge. If a game has 8 different cards you get 4 random drops.
4) Free card drops can be dupes.
5) Any more cards needed to craft the badge have to be bought on the market or traded with friends.

Yes and Yes.

As far as Steam is concerned you are actually running the game.

Why would they allow you to get drops for games that you do not own?

You need to own the game to be eligible for the features of that game.

Try using the Zip file from https://github.com/jshackles/idle_master

It contains everything needed to install IM. Looks like it's having an issue getting the files from the IM website.