I'm not familiar with any Steam/Valve reason. Play time has no impact on booster packs other than playtime being the requirement to receive cards and receiving all your free cards being the requirement for booster pack eligibility.

I vaguely recall some achievements that require total amount of time. Some giveaways run by 3rd parties may care about playtime. (E.G. Company X makes a sequel and accounts with 300+ hours in the first game are eligible for a promotional giveaway)

After just 1 drop? Any particular reason you feel this would be a meaningful change?

Does your Badges page actually say "2 card drops remaining" or does it just show that you are missing 2 cards from the set? The yellow boxes in This Image show you where to look.

If you have remaining drops, are you playing a game while you idle? Running multiple games causes the drop rate to plummet to abysmal levels. There's been a few posts recently that it'll stop drops completely, but the details on those test are vague at best.

Playing the game only gives half (rounded up) of the number of cards. 5/2=2.5 Rounded up to 3 cards.

If you want the remaining cards you need to trade with other users, purchase them off the Market or wait till you receive a booster pack.

How long it takes depends on how many games you have drops for and which games. Each game requires 2 hours of playtime before you can receive cards from playing/idling. Once you have 2 hours of playtime, the rate you receive cards depends on what the game's developer set it at. Most games are set at 1 card every ~30 minutes, but some games are set at 1 card every ~1 hour.

Yes, it will count has having multiple games open.
No, it will not speed up the acquisition of cards. Running multiple games at the same time drastically reduces the drop rate.

Yes, that's normal. To prevent abuse of the change in refund policy (I.E. play till you get cards, return game) Valve added in a requirement that you must have 2 hours of playtime before the normal drop rates start. For that two hour window it doesn't matter how many games you have running so stacking multiple games is ideal. Once you get to the normal card drops, running multiple games drastically reduces the drop rate so running 1 game at a time is better.

Double check your Badges page to see how many drops you have left? Looks like you have 2 non-F2P games and more than enough playtime to have earned your alloted free cards for them. If you're not sure what to look for, This Image might help. The yellow boxes show how many drops are remaining for each of the games, notice that Binding of Isaac is listed as having 0 drops remaining which means further idling of that game will not result in additional cards.

You should be good idling multiple games for the first 2 hours since that period is just to prevent abuse of getting cards and then returning the game (you can't return a game with over 2 hours of playtime). After you get past the initial 2 hour window, idle each game separately since running multiple games will drastically reduce the drop rate.

There have been fairly recent reports that running multiple games will now completely prevent card drops but there's nothing official from Valve on the subject and I haven't seen any testing from the STC community.

According to the FAQ, it's possible using Idle Master. I've never attempted it so I can't verify if this actually works.
https://psteamcommunity.yuanyoumao.com/groups/idlemastery/discussions/0/615085406651320102/

Can Idle Master be used to pad my playtime of a particular game?

The steam-idle.exe application that's included with Idle Master can be given a command line argument of the appid of the game you'd like to idle. For example, if you'd like to idle Team Fortress 2 for playtime, you can simply run "steam-idle.exe 440" from a command prompt. There is no user interface for this, it must be done through the command line.