"I invited them to provide the samples" is correct, but rather formal. Ok, if you want to be very polite or formal. Otherwise, I'd suggest using 'ask' ... "I asked them to provide the samples".
"I invited them to provide the samples for." is incorrect. It is correct if you follow 'for' with what the samples are for. ie. 'test', 'experiment'. "I invited them to provide the samples for the experiment".
As with #1, be aware 'invite' is somewhat formal. Ok if that is the intent or desire, otherwise use 'ask'.