hi greeneggs!
@1.: what is important is the relative potsize. on NL 1000 a 30$ pot is still small 
thus you should take into account whats the ratio between your remaining stack and the pot on the flop. usually if we raise preflop´and get one caller the flop pot will be ~7-9BB. in those cases I always recommend to bet 2/3 pot. with a starting stack of 20BB and a raisinsize of 4BB we have ~16BB left and the pot is as said before ~7-9BB. therefore the ratio between remaining stack and pot would be around 2:1. if we now bet 2/3 pot we protect our hands good enough - even if our opponent has a good draw he can't win much more from us, he doesn't have much implied odds.
also if we are unimproved on the flop we bet enough to make our opponents fold often enough; and on the other hand (which also applies to your 2nd question) we don't risk too much and can still fold if we didn't hit the flop.
thus, always if you we're the preflopraiser you should cbet ~2/3 Pot.
but in an unraised pot things change. if you get a freeplay in the BB with 2 limpers the pot on the flop will be ~3-4BB. but you still have ~19BB left. the ratio is now ~6:1. the result is that your opponents can win more from you (they have more implied odds). due to this I recommend to always bet 3/4 Pot to potsize if you have made a hand justifying the bet in an unraised pot (see the strategy section)
@2.: maybe you already got the answer of course its possible to push all-in if you have made a good hit. as a shortstack thats not such a big fault. but this has crucial consequences. you will only get called by very strong hands since your opponents won't call weak hands for such an expensive prize. in addition making this play does not give you the possibility to make a continuation bet if you don't hit. such a push cbet woul be too expensive. however if you always push with your good hands and cbet 2/3 pot with your trash hands then you will get predictable. so, the 2/3 pot betsize is a compromise which allows you to make continuation bets (which are creating much value if applied correctly!)
I would only recommend to push directly as a continuationbet or valuebet on the flop if you we're the preflop aggressor if your remaining stack is smaller than the pot or around potsize.
if you get a flop call with your top pair and still have money left on the turn I would push if my remaining stack is smaller than the turnpot and if its bigger I would bet 2/3 pot again.
I hope I could answer your questions greeneggs. but, one last thing. the things I mentionend are basic SSS strategy rules. but every poker hand is different and therefore there are many different ways ro play a hand. the basic rules are not always correct - only pretty often.
so try to learn as much as you can and improve you're play. you will see that its not always the best play to cbet 2/3 pot if you we're the preflop raiser and just have one opponent on the flop. as well it is mostly correct to bet the turn again and call a turnraise with your flop-top pair as long as your stack is normal sized. however if you doubled up before and now have 40BB in your stack things may change.
regards,
xarry
