Does the prayer of a person praying alone in the mosque while the congregation is praying, or of a person who prayed alone in the mosque after the congregation has finished, become invalid? Is it obligatory to repeat it? What is incumbent upon someone who does not remember the number of these prayers? And should the Friday prayer be repeated as Dhuhr prayer for the same reason?

Your prayer in the hotel is valid, and congregational prayer in the mosque is not a condition for the validity of the prayer.

Whoever prays alone in the mosque while the congregation is being established, their prayer is valid, though it is considered a wrongdoing.

Praying in congregation in the mosque carries a greater reward. However, if the Imam does not observe the minimum level of ṭumaʾnīnah (tranquility/stillness), then he is considered to have violated one of the pillars of prayer. This is considered an excuse for not praying behind him or for not attending the mosque.

If the Friday prayer is missed due to this violation, it should be re-prayed as Dhuhr prayer, four rakʿahs.