Aircraft behavior, vertical speed

Your first question:
If you "clear all weather" in your settings you should be able to trim the 172SP into a perfectly stable flight.

Second question:
Someone else will come along and tell you sooner or later 😉

Getting it perfect even in fair weather conditions can be difficult, but it should be close enough that it isn't a problem. Try adjusting your power just a little bit and you should be able to get it very close. I think the problem is that no matter what method you use to trim (stick buttons, mouse or keyboard) it just isn't perfect.

I usually have to make an occasional adjustment, but it isn't a problem for me.

I don't know the answer to your second question but here is one way you can check your speed at landing, just do a replay and watch your speed. During the replay you don't have anything else to do and that is a good way to critique your landings..

in real life you can trim the aircraft so that it is perfectly trimmed but you will not be able to take you hands off the yoke for long periods of time without pitch oscilations. in good weather you might get away with 20seconds but you will still need tiny adjustments with the yoke.
i guess they are trying to be realistic.

Also, in real life, the center of gravity of the aircraft is constantly changing as fuel is burned. This requires frequent small adjustments in trim. I don't know if FS9 is purposefully doing that to represent reality but it is what happens flying the real C-172.

As the pre3vious poster said, if you neglect controlling the aircraft for any length of time, you will be able to practice your "recovery from unusual attitudes" techniques.