As long as you interview other places on your own time, no problem. Your time is your own. I'd only see an issue if you were interviewing while you were supposed to be at your current job.
You can always leave your current employer off your resume. Even if you ask a potential future employer not to contact your current one, that doesn't always happen.
There's no rule that says you're limited to just 2 weeks' notice. You can give them 3, 4, 6, or whatever number of weeks you want, though 2 weeks is a courtesy.