Does your Badges page say you have drops left for those games? The yellow boxes in this image show what you're looking for.
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=503188239

Free-to-Play games do not give any cars just for adding the game to your Library, you must spend 9$US for each drop. Non-F2P games give half (rounded up) the number of cards in the set. Duplicates will count against your allotment of free cards. Trading/Selling/Using those cards will not grant you replacement cards.

Are you idling multiple games at the same time? That has a disastrous impact on your ability to receive cards.

Some(most?) account are required to have 2 hours of playtime before normal drop rates start for that game.

Last I knew, the default behavior is to idle all (up to 30) games simultaneously until they have 2 hours of playtime, then idle them individually.

Try right clicking on Idle Master and selecting Run As Administrator.

Not without major changes to the Steam mobile app. In a nut shell, the process is...
1) Idle Master tells the Steam client you're playing GameX.
2) The client tells Valve's servers you're playing GameX.
3) Valve's servers periodically give you cards

The mobile app is unable to accomplish step 2.
You could look into some form of remote administration to periodically poke your desktop. I use TeamViewer for most of my remote administration but Chrome Remote Desktop is another alternative.

According to your Badges page, how many drops do you have remaining? The yellow boxes in this image show the proper location to look at.
https://psteamcommunity.yuanyoumao.com/sharedfiles/filedetails/?id=503188239

Yes it's fine. Been the default behavior since June when Valve started to allow refunds and so far no reports of people getting banned. If you're concerned, there should be an option in Settings to idle completely sequentially.

Do you have less than 2 hours of playtime in those games? By default, Idle Master will run all your games (up to 30 simultaneous games) until they reach 2 hours of playtime, then it will idle each game individually.

Idle Master will idle new games, there will be no update to include new games since it's not needed. Idle Master doesn't maintain a list of games to check, instead it downloads http://psteamcommunity.yuanyoumao.com/my/badges/ and checks to see what games are have drops remaining.