Sorry to be harsh but...
You have to get a really tough solicitor. My now DH had a useless solicitor for his divorce and it has been hard for him. (She left him for another man).
Go for a pension sharing order, especially if he has a good scheme. This will benefit your DD in long run. I got one as I have a serious health condition which could limit my ability to work in later life. This means I will not have to depend on my daughters financially if that happens. My eX died a few years after we split and left everything to his new DW. My daughters got nothing. But they will get something from the pension when it falls due to me.
Divorce law is no longer based on blame. The fact he cheated will make no difference to the settlement, but if he does get his MYW pregnant he will be seeking to reduce your DDs maintenance.
His DM will be on his side. Stay civil to her, but keep important info to yourself. There will be time for rebuilding that relationship if you want to after things have been settled. My exMIL found it tough during divorce, but we kept a fair relationship going for years until she passed away. He had cheated on me for years and she was very conflicted about it all.
Your lovely male friend - take care this isn't used against you by your STBxH, even his family and friends. Every trick in the book may be used against you.
You are a mother of a daughter. He is unlikely to be that bothered about making sure she is provided for. Sadly many men often don't have the same ties to DDs as DSs after a divorce.
You'll find out who your real friends are too, which is a gift that doesn't feel like it at the time but really is.
And be careful of the predators who are on the look out for newly divorced women. They can be very charming and shockingly, many are married. They know you will be out of practice with dating and still raw, and they prey on that.
That said, you will be fine in the end. Take the great advice on here, be kind to yourself and your DD.