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Is there any way to get a free gold, platinum, or diamond membership?

I do not expect player's to give me a membership but If I got one I would be extremely grateful and I would use it as much as I could and give a shoutout to the player on my PF and team page.

You can just use the free ways instead of membership. Instead of buying for lessons, you can search up some the title of what they're teaching in google/YouTube. There's also a lot of lessons in YouTube. You can check GothamChess's old videos, remote chess academy, etc. Instead of game reviewing every game, you can open the game you have reviewed and just move as you're playing. I mean you can try to play with yourself as best as you can then the engine will tell you about that move
Merlin Pendragon got a free unlimited diamond membership by playing in chess.com for continuously 4 years.