it does not seem that many.
Dík or Díky for "thanks"
Děkuji for thank you
Děkuji vám/ti for thank YOU
That is about it. For a native speaker they only seem like two option. For a non native it likely looks like a plenty.
There, of course, is also a super colloquial "tak Ď". Literally "So T" t as in thanks.
My mother pronounces it more as de-co-you. I'm not sure if that's a faulty part of beta or differences in accent
It is a completely different word. :-)
Díky = thanks; děkuju (this is what your mom says) = thank you.
Some natives also use what sounds like "Dekujiamotz" meaning thanks a bunch... Not sure how to spell it but thats what some natives taught me when I went there
"Dík moc" Thanks a lot
"Děkuji moc" Thank you a lot.
"Děkuji vám mnohokrát" Thank you manytimes.
"Děkuji vám pěkne" Thank you nicely
Just a few nitpicks on the English side, to avoid confusing anyone...
"Thank you a lot" would not normally be used, but the Czech phase indicates how it differs in formality from "Thanks a lot."
"Thank you many times" would more likely be phrased as "Many thanks."
"Thank you nicely" would not be used, but I can't think of an alternative at the moment. (If I do later, I'll add it.)