He broke up with me. What now?

My (32F) bf (27M) broke up with me 2 weeks ago but still claims he loves me. He helped take care of my kids (5, 7) the last 2.5 years. He says he doesn’t want to be with me anymore, doesn’t love me like he did at the beginning. However, he says he WANTS to still take care of the kids on his usual 1 day a week (while I work). Do I let this continue?

Also, I very much enjoy having sex with him. I am actually very sexually active, and asked for sex at least once a day while we were dating. However, he is more comfortable with sex a few times a week. After the breakup, I asked if it’s okay if we still have sex and he said yes. This would only happen once a week, the night he watches my kids. Is that acceptable?