#2 feels less natural but not exactly wrong. It has the same meaning as #1.
#3 is not natural.
Note that the choice between "on" and "for" depends on the role of the phrase within the sentence. For example, you would say "that was a mistake on my part", not "that was a mistake for my part".
Why not keep it terribly simple and say either " please accept my thanks also Paul" or " I would like to thank you too" etc etc. There are a number of ways to offer thanks without getting unnecessarily wordy. "From my part" does not sound right in this instance anyway.