Learn Farsi: او واقعا جوان است.

Yes, you can! Because the verb است (is) already tells us the subject is third-person singular (he/she/it), saying واقعا جوان است is a perfectly complete and natural sentence. Including او just puts a little more emphasis on the person: 'He is really young.'

The translation says 'He'. Could this sentence also mean 'She is really young'?

Absolutely. The Farsi pronoun او (oo) is completely gender-neutral and means both 'he' and 'she'. You only know which one is meant based on the context of who you are talking about.

Why does the word واقعا end in an 'n' sound ('vaaghe'an') when there is no 'n' letter written?

This is a special spelling rule for some words borrowed from Arabic. The word ends with the letter Alef, but it takes an '-an' pronunciation. You will sometimes see it written with a small double diagonal line on top of the last letter (واقعاً) to show this sound, but in everyday writing, that mark is usually left off.

Does واقعا (really) always go in this spot in the sentence?

Usually, yes. When an adverb like واقعا is modifying an adjective (like جوان / young), it gets placed directly before that adjective, just like in English.