Some people are fanatical about not splitting the infinitive by putting an adverb between the "to" and the main verb. Others (including me) don't find this a big sin. Perhaps because I grew up watching Star Trek, where their mission was "to boldly go..."
I am more likely to say "Try not to" but I won't say "Oh! No no no!" if I read "Try to not."
Google gives a whopping 138 million hits for "try to not" (including this thread!) and 93 million for "try not to."
However, I didn't understand the second pair of phrases. Can you write the full sentences?