In American English, pretty is more often referring to the beauty of a female or object while handsome is generally only used to describe males. He is pretty and she is handsome just aren't very common statements, though I have heard the former a few times. Cute is a more gender neutral term, but refers to a specific type of beauty, usually with some indication of smallness or daintiness, such as childlike or youthful features.
Fun fact: Snygg is actually a Swedish surname.
Back in the days, it was common or even mandatory for soldiers to be given a soldier's nom de guerre upon enlistment in the army. These could for example be some military nouns like Lans, Sköld and Svärd (Lance, Shield, Sword) or taken from nature, such as Björk, Ström and Berg (Birch, Stream, Mountain). Sometimes this name would be an adjective descriptive of some quality of the person. Thus, there are also surnames like Modig (courageous), Rask (quick), Sträng (strict, severe) or... Snygg. Which used to mean something like "petite", but changed meaning over the centuries to todays "hot" or "handsome". With time, they became family names in the 1800s and thus we today have a handful of soldiers' names being perfectly normal surnames today.
A friend of mine actually carries the surname Snygg, and yes, he is tired of hearing that it's sooooo funny. :p
"-e" adjective forms work the same as definite adjective forms, except they're used for male nouns. It's a bit of a leftover from older Swedish where there were both feminine and masculine genders.
It's only used before definite singular nouns, so:
"Den snygge mannen", but "En snygg man" and "Mannen är snygg".
A bit of "useless information" for those who like that kind of thing --
The words snug (English) and snygg (Swedish) are almost certainly related. The original basic meaning of the former word was "compact, trim" and that of the latter "neat, tidy". By extension of meaning snygg came to signify "handsome", and in Lancashire dialect snug means not just "tight(-fitting)" but also ..."handsome".
'very' and its Swedish counterparts such as väldigt, mycket etc mean 'to a large degree'.
'so' and så can mean either 'to an extent that is clear from context' or 'to a large extent' but if it means the latter, it's more emphatic and emotional than mycket/'very'.
This works pretty much the same in Swedish & English so go with så for 'so' and mycket etc for 'very'.