Actually it's two sentences: I took my dog inside. Once inside, I felt safer.
The only thing wrong is that you need to put a space after periods and commas.
"asleep" = "sleeping" Don't know what else you want regarding adjectives.
Rohit is
a better boy than Ram. OK.
He is the best boy in the class. OK.
a better boy than, the best boy ---- both are OK.
a bigger car than, the biggest car ---- both are OK.