couldn't we use "those boys are nice" as a translation?
"Nice" does not mean "hezký" when used for people.
Should it be "hezčí"?
Hezčí is the comparative form of hezký.
Why is beautiful not accepted?
We use the word "krásný" for "beautiful". It's stronger than handsome/pretty.
Is it allowed to use hesci and hezky?
'hescí' does not exist. Hezký, used in this sentence, would be non-standard Czech. You need to use the appropriate case ending.
Why not THESE boys are handsome? Wouldn't 'those' actually be 'tamci'?
TAMTI - the, those
TITO - these
No. The singular is "tamten", so plural must be in animate masculine "tamti"