Most of the time I would advise against moving in with a boyfriend too soon. This is the exception to the rule.

Take your boyfriend up on the offer, cook him a nice meal or something to say thank you and focus immediately on getting your shit as sorted as you can. You're going to need to talk to the police about what your sister is doing and get advice on how to keep a safe distance. They'll probably tell you to keep records of texts and phone calls, as well as file a report for stealing the car parts and router. Even if you don't want to press charges, I would make a report so if she tries to escalate they can act sooner and protect you.

Step up your freelance work/find a job to help support yourself (and, unfortunately, save up for that birth control/health insurance) and, when you are a little more stable, move out of your boyfriends and into a seperate house so you guys can start dating normally again. It's going to be really tempting to stay, especially if it feels like things are going well with you two but you need to know that you can manage yourself financially and emotionally so it doesn't feel like your entire world is coming down if things don't work out. Being dependant on him for longer than you need to be or making him feel like you are taking advantage of his generousity won't be great for your relationship but, right now, you really don't need to worry about that. Focus on getting on your feet and you guys can go back to dating like you've been together 3 months when all this has calmed down. :)

You need to do plenty of freelance/find a new job. At this point, just about anything will be better than what your sister put you through so don't worry too much if you start off working something minimum wage that doesn't entirely suit you. It sounds like you have skills from the business that will hold you in good stead so I'm sure another business will take you and appreciate you for the hard worker you clearly are.

You also need to make yourself untracable to your sister. Do not tell relatives where you are if there is even an outside chance of them passing that information on, think carefully before you register anything to your boyfriends new address and consider putting a freeze on your finances so your sister can't hit you there. Get off any shared bills and put them in your own name. The police can help you with more specific safety information - listen to them. If they suggest something that seems harsh, don't dismiss it automatically. What your sister is doing isn't just technically illegal, it is abusive and I would strongly encourage you to consider a restraining order if the police say you could use one in your situation.