If I assign several dwarves to same room, for example a large dining room where everybody has a chair, how does it affect things? Would it be better if everyone gets their own separate dining room?
Overlapping "rooms" reduces their value, and thus reduces the happiness that can be derived from them. You should also consider if you need to assign the room at all.
In my personal experience, it's not worth assigning dining rooms to anyone except nobles. Just create a big dining room with lots of chairs and tables, make a "dining room" off a single table, and engrave the whole thing. Instant Legendary Dining Room. Anyone who doesn't have a dining room assigned (i.e. anyone not a noble) will use the big dining room and get lots of happies.
When it comes to bedrooms, you have some options. I personally find it's worthwhile to give everyone an assigned bedroom with a bed and container. Owning furniture makes them happy, as does having a place to put their stuff. However, it's a fair bit of work to make a hundred furnished bedrooms, and it's tedious to assign them.
You may prefer dorm-style bedrooms to make life easier, but these will make the dwarves less happy. If you go down this road, just put a bunch of beds in a room. Assigning lots of little "rooms" within the physical room won't gain you much.