Is it obligatory to return a towel taken from a hotel in Makkah, as compensation for a personal towel mistakenly taken by hotel staff, and for other items that were broken?

You must demand your towel from the hotel management or its replacement. If the management does not respond and you find no way to reclaim your right except by taking its equivalent from the hotel, then you are permitted to do so.

As for what the hotel employee broke by mistake, he is not liable for it if it was without negligence. However, if it was due to negligence or transgression, then the liability falls upon him, not the hotel management.

You must return the towel you took to the hotel and demand your towel or its replacement. If they do not respond, you are permitted to take what equals your right without their knowledge. As for the broken item, you may demand compensation from the employee if he broke it due to negligence; otherwise, no.