Well, first off, don't panic. At least you don't live together. Just take it slow - they need to get adjusted to his home and you need to see how he parents and handles any issues they might have with you. You should be sure he insists they treat you with respect. You should also be clear with him that you do NOT intend to step in as mother - that the parenting is on him, period, all the time. That way you can get to know them in a positive way, without having to step in and discipline.  Do not move in until you see all these conditions met: he can parent them, he doesn't allow disrespect of you or him, and he doesn't expect you to be their mother.

The best thing you can do right now is not get involved. If you can take a pause on your relationship (not break up, just not go out and hang out right now), that would be the best course of action.

Your BF will need to get his kids settled in school, find childcare (maybe), get them any paperwork for visas or citizenship if they don't have that already, get them set up in therapy, move them in, set up a new routine...

You get the picture. Right now, you can be supportive of your BF by offering to bring over meals or paying for someone to come and clean the house. Your BF can tell the kids who you are, but staying in the background while they process their grief and your BF gets them set up is going to be better than you jumping in to try and save everyone.

This is going to be hard for a while. Take a BIG, DEEP breath. Even if your BF tries to pull you in, kindly tell him no, that the relationship is secure, and you're giving him space he needs to help his kids. If he has something specific that he'd like you to do that DOES NOT involve his kids (like making a meal, or picking up dry cleaning), then help him that way.

Do NOT. Jump in and start playing MoM.  Do not start taking care of  SK. Let SO get settle in. Let him get child care. Let him start cooking and cleaning.  
See how you fit in in a few months 

A lot of woman will feel need it,  and jump in with both feet.  Then feel disrespected latter 

In loving memory of sayno, I am going to go with.....RUUUUUUUN! 

I just want to say, be prepared for anything. Even before BM's death, there must have been some deep dysfunction if you have been dating over a year and 2 kids over 10 don't know about you. You have no idea how he parents, no idea what you are getting into. This is a terrible situation for the kids, but you also have to protect yourself by knowing your worth and setting boundaries. It's ok if you realize this relationship is not for you if you see major red flags. You can search this site for a list of things to look for. Definitely be compassionate and understanding, but, beware. This sounds like a very difficult situation. 

Do you want an instant family? If not, save yourself and move on.

If you are amenable to giving it a try, before your BF gets back with his kids have the household standards of behavior and performance posted to review with BF as soon as he walks in the door. As soon as you present them to him, have him present them to the kids.

10+ is long past old enough to be held to compliance to appropriate behavioral and performance standards.  

Get these kids into therapy to help them navigate the grief and change processes that thew will be going through.

Do not mistake acceptance of behavioral or performance crap from either the kids or your BF for kindness.  Be kind, but be assertive.  Grief is no justification for the kids to be disrespectful of you or your home nor is his kids' grief justification for your BF to treat you in any way other than with respect as his equity life partner.

Just my thoughts of course.

Take care of you.