In the attached pic if there was a white stone in F3 position would white keep those stones and all the black stones in the lower right be white's prisoners?

No, White is dead.

Thank you! I'm new at this and trying to get a grip on scoring. What app is that you were using?

I created the sgf file with CGoban, the usual KGS client.

Do you know about false eyes yet? f3 is a false eye so filling it in doesn't help white.

Some more interesting changes for you to ponder (in combinations too):
- what if e4 was a white stone? that would make the f3 eye real.
- what if j1 was a black or white stone?
- what if g2 was a white stone? That makes the f3 eye real AND means h1 can only be a false eye.
- what if black's turn to play?
- what if white's turn to play?

There are so many things to ponder in this game, that's what makes it so amazing!

That raises another question, if white played F1 would that make the black stones on thrower left prisoners of white?

I am not sure I understand your question, but if White F1 then White is still dead.

White is dead. Nothing White does can win the life and death battle in the corner, saving White by capturing Black, if Black plays correctly.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Thank you, sir!