No advice but lots of thoughts and questions that might help you think it through.
The mother's approach seems awfully casual. Is it possible she is just looking to "park" him somewhere and still expects to be able to drop in to be mommy now and then?
Are you willing to take both? Are you willing to have a long-term open relationship with the mother? Facilitate the sibling relationship despite issues with the mother? Are you willing to cut the mother or other family members out of your life if they do not accept you as the parents or disrupt your parenting of the child/ren?
Do the kids have issues that you know of or the likelihood for certain issues--drug exposure, fetal alcohol, etc.? Has either any red flag behaviors--fire play, hurting animals or other children when not angry, etc.? Are they on Medicaid (state healthcare) now? Are they eligible? Would you be able to maintain their eligibility in addition to putting them on your insurance?
Are you sure the bf is the father of both?
Are you interested in having a long-term open relationship with the bf and/or his family?
How old are you? Have you looked after little ones lately? I'm asking 'cause I'm an "old" mother, and they do NOT keep me young! They age me greatly!
No kidding, it ain't so easy....
How much will the process of adopting one or both of the kids disrupt your household? Will you have to quit work or cut back? Will it affect your older children's post-high school plans?
That's probably a good start. All wise decision-making rational thinking aside, however, do you want to give these children a home in their family? Are you willing to do just do it and not look back? Will you keep their trust and really parent them and protect them?
Been there, done this. It is not easy. For ourselves, it felt like the right thing to do, we just closed our eyes, crossed our fingers, and did it. There are moments of great joy, moments of deep regret, but mostly an abiding sense that this is right.
Good luck with this, I hope things work out well for these children.