Мать завезёт меня на работу. "my mother is dropping me off at work today."
Мать завезла меня на работу. "my mother already dropped me off at work."
Мать завозит меня на работу. "my mother drops me off at work every week."
Я лечу на Украину. "I am flying to Ukraine today." - OR Я прилетаю на Украину сегодня.
Я прилетел на Украину. "I arrived in Ukraine already." (your sentence meant that you're flying on a plane and have just approached the Ukraine's border).
Я летаю на Украину. "I fly to Ukraine repeatedly." (the verb прилетаю doesn't convey the idea of the constancy of the fact thay you fly to the Ukraine repeatedly).
Мать уходит от меня. "My mother is leaving my home right now."
Мать ушла от меня. "My mother already left my home."
Мать уходит от меня. "My mother leaves my home every day."
I think that мама would work better in your sentences