"Raj is very sad."
Translation:राज बहुत दुखी है।
Just gotta remember which ones are which as you learn them.
Usually adjectives that don't change with gender are easily identifiable because they don't have any gender endings, like खुश, लाल, साफ, and सफेद. दुखी is the same category of those adjectives that don't change, and the fact that it ends in ी is purely coincidental.
राज बहुत उदास है। would have been correct.
बिलकुल doesn't exactly correspond to 'very'. It can be used to denote the intensity of the emotion in which case it means something close to 'absolutely' or 'completely'. However, depending on the context, it also has other uses. For example, if you tell me 'राज दुखी नहीं है' and I revert with 'राज बिलकुल दुखी है', I'm not using the बिलकुल to mean 'very. I'm using it to indicate that I'm disputing what you're saying.