BMW Repair: 1995 BMW 318ic -shuddering during car running idle, bmw dealership, bmw 318i

Question
I apologize in advance if my questions are uneducated.  Neither my boyfriend or I are very knowledgeable about cars.

My boyfriend and I purchased a 1995 BMW 318i Cabriolet from its second owner about 6 months ago.  Recently, we both noticed that when the car is running, but idle (for example - stopped in traffic) - once in a while the engine (?) appears to shudder for 30 seconds, and then the shuddering stops.  Also, we're not sure if this is related - but during his recent oil change - the dealership noted that the check engine light is always on, although they didn't think it was a major mechanical problem, but something we need to get checked during the next oil change (in a month or so).

1) Are both problems related?
2) if not, we're curious what causes both issues?
3) will we need to take the car to the BMW dealership to address the problems or can a mechanic (not BMW specialized) be able to diagnose and fix the problems?
4) what sort of repair costs (if any) are we looking at?

Thanks in advance for your consideration

Answer
Well whatever causes the shutter has set the check engine light. You need to have it checked as it could be an ignition problem and could cause more problems.The local dealer would be nice but costly,a good import shop is also good.The cost will vary as to where it goes,to just check the light for the codes given probably about an hours labor although it does physically take that long to check.