when writing a formal essay and having 2-3 lines of empty space between the end of your paragraph and a new page, could I skip those 2-3 lines to start on the brand new page or no?
Are you writing your paper by hand? Are you using a typewriter? Or are you using a word processing program on a computer?
In Word and other word processing programs, there's "widow and orphan control" which is usually turned on by default. The program will decide for you unless you turn that control off.
If you turn that control off, you can decide when/whether to start a new page. Also, if you're writing by hand or using a typewriter, you can also make such a decision.