Is it biblically appropriate to call God, our Heavenly Father, as any other term or name other than one that relates to the Word. Such as calling Him the 'Man Above' or the 'Big Man' or other terms as such.
Well -- considering it Is God you're talking about. Respect for who He is would be good. Almighty God would be appropriate. The last two terms would not be showing respect.
Respect is something you feel inside. What may seem disrespectful to somebody else might in fact have more devotion and depth of feeling in it.
Only you (and God) really know with what respect and reverence you are using those words. God knows better than the people who judge you.
YHWH which is kinda hard to articulate or pronounced. Jehovah will suffice and if I got that wrong he is a forgiving god. So I wouldn't worry about it too much