Connecting to neutral wouldn't hurt, but it won't make any difference either. Do not connect it to safety earth/ground. That's a bad idea and is against the safety regulations in most jurisdictions.
I'll just point out that many "jurisdictions" REQUIRE the neutral to be bonded to "safety earth/ground" at some point in the installation, typically the building entrance.
Not really, combining Earth and neutral is only at the source, which in our case is the distribution transformer.
In TN-C system you get earth (PE) and neutral (N) combined, designated as PEN conductor from the distributor. Per IEC, PEN conductor is green/yellow. If you need neutral, you seperate them in such way that the PEN is directly connected to the PE bar and then linked to the N bar. At this point you make the TN-C-S type of system.
After the point that PEN is seperated into PE and N, they should NEVER be combined again.
Minimim allowed cross section of the PEN conductor is 10mm2 for Cu.
TN-S: you get seperate PE and N, no joining allowed. You join your own PE with the distributions PE.
TT: you get only N from the distribution, PE is yours, no joining allowed
IT: only 3 phases from distribution, no neutral, your own PE