You are close but not quite there. English is a very quirky language. Your example sentences should read:
One of my friends is a lawyer.
One of my neighbours (neighbors if you use American spelling) is a doctor.
A number of students are going to a competition. (Could also be The number of students going to the competition is three.)
The number of students seeking admission has increased.
You had the basics but a few of the finer points were missing.
ya.two type of english is continue British and USA.Where you find fault in my example I do not understand