Can a tenant be held responsible for property damage that was caused by a guest? And how much time by law does the tenant have to pay the damages if the tenant is financially responsible?

Yes of course they are liable for anything that happens to the property under their control.

They have to pay for the damage at once, Or actually have it fixed at once, how they pay the repair person is not the landlords issues.

If it is not paid at once, the landlord can sue and get a judgement for the damages, and even seek eviction.

Yep, I agree and this will be true even if your guest refuses to help you, its your responsibility. If the damage was huge and the guest refuses to help pay you could consider suing the guest