English question, does it appropriate to change the tense of “collaborate” from present to past in following sentence?

I think maybe it is "We heard OF heroes..."

Also "I have a little doubt, are there any reasons to change the tense..." would sound more natural to an English speaker as "I'm not sure. Wouldn't it be better to change the tense..."

There is a reason to NOT change "collaborate" to "collaborated". In English, the phrase "rather than collaborate with the Nazis" is considered to "depend upon" the preceding phrase "who sacrificed their lives". The time-sense of the overall construct "...heros who...the Nazis" is established by the "-ed" in "sacrificed". Once that is established, everything else described in the subsequent dependent phrases is always kept in the present tense. It allows you, as a witness, to enter into an event that took place in the past. Once you have entered into that time & place, everything you learn about it (within that dependent phrase) takes place in YOUR present. Notice though - that only applies to the description within that sentence alone.

"The engineers designED the rocket to GIVE the astronauts a survivable ride, instead of ACCELERATING at a crushing rate. Their choice providED a chance for success, but complicatED the control mechanism greatly."

The action of the engineers is in the past. But if we place ourselves at the engineers' elbows in that past moment, what they WERE doing becomes what they ARE doing, and everything that flows from or contributes to what they ARE doing becomes part of our PRESENT and is therefore in the present tense, for the duration of our visit to their past moment (which expires at the end of the sentence). Once we pass the dot at the end of that sentence, we are back in our own time, and the engineers are in our PAST, so subsequent sentences again assume the past tense.

In this sentence, the word 'collaborate' is not in the present tense. It is an infinitive, and thus would not change.

Collaborate is correct. Collaborated would be incorrect.