Most proxy sites do not allow account sign ups, javascript etc. I don't think using a proxy is a very good idea, i find that alot of abers using proxies etc find the same and you both get frozen.
Game cheating is relatively safe in terms of just getting the 1,000np. Depending on the game getting over the review score can be safe too since some games TNT can't tell if its done by cheats (i think) whilst others will just be instant freeze, especially if you send score quick and yes they have timers.
Yes there is a certain score that they automatically review, i think they can only check if you were cheating by the score (if its just impossible to achieve) and the time taken to achieve that score (like you got the score too fast for a legit player).
Don't really play or cheat at games much these days but last time i was frozen was the cheat for jelly blobs of doom where you just grow massive and i got a score of like 10,000 in 1 min (I didn't check high score or check review score), was frozen as soon as they checked. Other games i've had reviewed but i don't think they can tell so i was never frozen for them.
As far as i know your IP should change after a while, about the router reset i'm not sure on a static IP but it certainly works for me but i have a dynamic IP.