And please tell me, is it better to take hardened surface fragments from active titans or destroyed ones ?
Define “better”. For Engineering it does not matter where you got the materials from.
At an active Titan you can gather them much more quickly, but it is also more dangerous and you need a different ship build (caustic sink + TG pulse neutraliser just to get there).
Arguably the easiest way to gather them fast is to do it during the last day of a Titan, when the pulse neutraliser is no longer necessary, the Titan can no longer zap you with its blue field and most Thargoid ships are busy evacuating rather than patrolling. Of course, the next opportunity is going to be no earlier than in about 3 weeks
(BTW, gathering stuff at an active Titan is best done
not in open; having random CMDRs in the instance usually means aggroed Thargoid patrols that will tend to search aggressively around the Titan and can spot you even if your heat level is ≤ 2%.)