it is okay to use "Yoroshiku Onegaishimau". because if it is in english it means "Please treat me well". for example, if we introduce ourself in our new class or work. we will introduce ourself and use "Yoroshiku Onegaishimase" at the end of the introducing...

I think it is appropriate to end message or letter when you request something to someone. I often use" yoroshiku onegaishimasu" in my business email.

Seems fine to me.