is there a difference between saying "... jest taka ciezka" or "... jest tak ciezka" ?
No, but "taka" is an adjective so it depends on a noun - taki/taka/takie/takiego/taką/takiemu/takiej etc. "Tak" is an adverb so it always has the same form.
I don't know. (And I'm Polish). Literally "taka ciężka" means as heavy as we know it is. I feel like there might be a slight change in accent TAKA ciężka, tak CIĘŻKA.
"taka" can be compared to "such"
"tak" can be compared to "so"