If you have an Ike and Hector, you can literally just smash the refresh button for the Training Tower until you see all Blue or all Green units. You just throw Ike/Hector in front of them, bring a healer, and you're done. It might take some time refreshing, but it's not that hard (ever since the introduction of the refresh button). As for the class specific quests, I feel like most people struggle with those anyway. I imagine most people bring like 1-2 strong units and refresh colors until they have an easy matchup and just carry 2 weak units of the same class.

The infantry quest should be on the easier side since most units are infantry units anyway. You also stated you have Ike, so if you just refresh until you see a 10th stratum with like 3 enemies (i.e. 2 green 1 healer) you can just dumpster them while carrying along 3 weak infantry units (though I imagine you have strong ones as well).

It seems like you have a lot of strategic area to improve on, haha.

As for GHB and other challenges, there is this wonderful site (http://yaycupcake.com/feh/) that compiles solutions. People often have solutions using mostly 4* units or free units only (with minimal/no SI and no merges).

Use the resources that are available to you if you care so much instead of complaining when it doesn't even seem like you've tried.