"A table for three people."
Translation:Una mesa para tres personas.
It is para because when you use "por" here, you want to exchange the table in return for 3 people, I guess those times are long gone. You should use por when you want to buy a table: Una mesa por 2000 pesos.
Could one say "una mesa para tres" for short knowing that people are involved in eating at a restaurant
Yes. You could even say "mesa para tres" and it would be just as understandable.
No, la gente has no plural vorm. Hay mucha gente en la calle. There are much people on the street. La gente caminan por la calle. There are people walking on the street.
No, they are 2 different words, I'm not native, a good way is to find some video about this topic on youtube and immerse yourself by looking over and over again. Here is one I used : https://www.youtube.com/watch?v=1UsHmPkUx_o&t=171s