The answers are no, no, no, no, and no. Here are a few good answers to related questions:

• October 2020, most important replies by u/Barely_a_Live_1 and u/toldinstone. Yes, they walked up Mt Olympus regularly; the clearest evidence of this is on the Ayios Antonio peak; belief in the literal physical presence of the gods there isn't justified by what we see in the evidence; 'Olympos' has a dual meaning, referring to the physical mountain and the heavenly realm.

• August 2019, reply by /u/toldinstone. Similar to above.

• September 2018, reply by /u/Muskwatch: comparative evidence suggests that going up mountains should be seen as an entirely normal thing.

• January 2013, reply by /u/Daeres: another post on Olympus' dual meaning, with both metaphorical and physical aspects.

The simplest and most salient answer is: walking up Olympos (not climbing) was a regular thing. There were regular offerings to Olympian Zeus on at least one of the peaks (Ayios Antonio). We've got no evidence of any taboos or laws to regulate visits. I think there's some reason to infer cult activity on Profitis Ilias as well, on the north side of the mountain, which is the main peak when seen from the sanctuary of Olympian Zeus at Dion; plus there's a 15th century Christian cult site there that may have been built on top of an older cult site.

It's probably also worth making it clear that walking up Mt Olympos doesn't require climbing or any special preparations beyond basic fitness. The walk can be done in one day if you're reasonably fit, and the summit is clear of snow most of the year.