So, can I enter High Hrothgat without being invited by Greybeards?

Nope, it is locked down until they call you

Then I have another question - I read in another forum that it's possible to do the MQ without dragons appearing at all - therefore not doing the quest for Jarl of Whiterun and killing Mirmulnir.
How is then possible to enter HH?Is there any other option during MQ?

Thanks!

It's not possible.

Only using console, teleport to parthunax, add clear sky shout(you dont rly need it if you teleport to him, but you will need it for the final fight against alduin) , and this is assuming parthunax would talk to you and would trigger the questline to find the elder scroll, if so you could avoid the greybeards completly, you would also have to finish the civil war to use dragonsreach, if you want to completly avoid the greybeards.

If you simply dont want dragons, simply never go to the golden claw barrow, near riverwood, or simply dont grab the dragon stone with the dragon burial sites, that way you can do every quest in the game without fighting a single dragon apart from 1 undead dragon.

Though the Golden Claw will be stuck in your inventory.
You're unable to return it Lucan Valerius, otherwise.

You can finish the dragon claw quest, just dont grab the dragonstone that is looted from the draugh defending the word of power.

Nope. Sorry, but no.
You cannot get rid of the claw unless you grab the stone.

makes sense, because you would need it to reenter the room were the dragonstone is, sooo simply dont start the golden claw quest, and its only 0.5 in your inventory, same has a health potion.

What I did to have 0 dragons was simply not do the goldenclaw and the dragon tablet quests, because it is when you deliver it to the court wizard in whiterun that the first dragon you have to kill spawns.

Thanks!