I think you are doing the best thing, because you do want the best for your boyfriend because you love him. But there is a difference between helping him with little reminders and forcing or as they call it nagging. Just don't be too pushy, because at the end of the day, him stopping will be his choice.
No. You're only caring for his health. It's not wrong at all but don't try to MAKE him quit. It's more difficult than you think, I know because I dealt with smoking a couple years ago. Just give it some time, he'll come around and realize how important it is to quit.
You can't control everything. It's his choice. It shows that you care enough to try and keep him from smoking. Some people prefer to smoke, if that's the case then there's really not much you can do. If he decides to smoke then just let him know it bothers you and let him know why.
Just remember, people that smoke really stink to non-smokers. (Other smokers are oblivious to the odor.) When in school, I would never kiss a smoker. The clothes stink, the car stinks, the breath stinks.. Move on to someone who cares.