‘People’ in ‘most people’ means people in general; ‘People’ in 'Most of the people' means people in a specific group. For example, most of the people I know don’t like smoking. ‘Most of people’ is not correct English.
Similar to 1 above.
The 1st one is good. ‘Somebody feels at home’ means someone is happy and confident in a place or situation. ‘Make yourself at home’ means make yourself act in a relaxed way in a place like you’re in your own home.
- For Teachers