It basically boils down to whether or not you dumped him.
If you want to be extra nice and not send him into a sad spiral, then maybe give it some time before you make a move on his friend. The sooner he gets over you, the better off he'll be.
If he is taking it slowly with the intention to be intimate again, to be dating another girl is not the way to go.
There are some questions about men that only a guy can answer.
If you travel in the same social circles, you might want to avoid being in the same place as your ex and the friend you want to date.
Really, though, you probably shouldn't be hanging out with your ex in the first place.
MEANWHILE, I have started showing interest in a mutual friend of ours.
I do not know whether or not he is interested, but he was my shoulder through the breakup and has been with me through a lot. Is it a bad idea to pursue anything with the friend?
The guy might want to wait a bit before starting anything with you out of courtesy to his friend. Also, be prepared for him to not want to get involved with his buddy's ex at all.) But you don't owe your ex anything. Even if he's jealous, he'll have to get over it eventually.
If your break-up is civil and you're still friendly, maybe give it a couple of months.
But there are a few points you should consider: First and foremost, your ex doesn’t really get a say in terms of who you can and can’t date.