Question 1: What are some other ways to say "it was confirmed there was no problem." in fewer words?
Answer 1: Hi. You can simply say, "Confirmed. No problem."
Question 2: Is it incorrect to say "It was confirmed no problem"? As in "It was confirmed no problem with this part." or "It was no problem in the test A."
None of the sentences are incorrect, but they are informal and would be correct in the context of a work report situation.
However, to be very certain that you're communicating clearly, it would be a good idea to say, "We can confirm that there was no problem with this part during Test A."
Note that you wouldn't place the word "the" before the phrase "Test A". The word "the" would be omitted.
I hope this helps. Good luck!