Your name hasn't specific English sounds like "th", because of it we can say it correct :)

Мне тоже нравится имя Скайлар. Красиво звучит. Легко запомнить и произнести.

As many people here have already said, you don't need to change your name if you don't want. I agree that your name sounds pretty cool in Russian) In my University, I met some сhinese and vietnamese students who use russian equivalents..so far one of them Jungian chose a russian name "Yuri". But others students who came from Ameica neither South America, prefer their proper names.

Скайлар - good name! I think the short version could be Скай (Sky)

nope, it is not natural, but if you want you can come up with a short version of your name (informal). it's common in Russia (Владимир=Вова/Володя, Елизавета=Лиза, Екатерина=Катя and so on)