I was hoping to hear more from you, before responding, but you can always respond here on this question thread and correct any misunderstanding I may have made about your circumstances.
You can be charged with acting together with your fiancé even though you never touched the stolen items. If it's reasonable for the store to believe that you had to have known what your fiancé is doing and that you assisted in some way with his unlawful act, you can find yourself arrested right along with him. This happens all of the time when, for example, a coupe of people are shopping together and one does the shoplifting while the other keeps an eye out for the store security guards, or is outside ready with the car for a quick getaway.
There's a big difference between what the state needs to make an arrest -- just a reasonable belief that you may have been involved in your boyfriend's criminal enterprise -- and what they need to convict you, which is proof of your involvement beyond a reasonable doubt. So did they have the right to arrest you along with your boyfriend? Yes, they arguably did. Will your case be dismissed? It's still possible, but as the DA didn't dismiss it from jump street but offered you a plea agreement, probably not.
Your fiance is probably looking at nothing worse than probation for this charge, but with two others in his past, he's skating on thin ice. If there's a next time, he may have to do some time. But as he hasn't had probation yet, if he can't get a large fine and/or a ton of community service, he should be able to get probation this time.
You, on the other hand, if you were interested in resolving the case in some way other than trial, might be able to get an adjudicated dismissal. That is, on a first arrest you'd be eligible for a diversion type of disposition. This is where you'd get supervised, do some community service, pay some fines, take anti-shoplifting classes and stay out of further trouble during your period of supervision. At the end of the successful completion of your conditionsl, your case gets dismssed. Or, of course, you can take the matter all the way to trial if they don't dismiss, and let the state try to prove that you were working with your boyfriend beyond a reasonable doubt.
As to the civil letter, the store has the right to go after you both civilly to help defray the cost of their theft insurance, surveillance system, store security guards and loss prevention department. However, despite the letter from the law firm, you don't actually have to pay the store unless/until there is a court order ordering you to do so. That is, you can ignore the letter and make them sue you, which for $150, they probably won't bother.
There's no advantage to paying the money, since you've been charged criminally already.