Ok, if they've already announced the League Cup final date you should be pretty safe as it'd be surprising if that was also an FA Cup weekend
I would think so but the FA never does anything smart. Sadly I may have to root for United and Fulham to get dumped out of the League Cup. Although I guess we could try and get tickets for that at Wembley if United made it again.
As I know you're a United fan, I would like to take a second to suggest paying up for the VIP experience for the game you are going to. I did it back in 2016 and it was well worth the extra few bucks to me. Now, granted me and my wife like to imbibe and we certainly had more than a few, but they give you three hours of open bar and food - and the food was actually quite decent. You have the chance to sit and chat with a lot of other strong United supporters that often times are visiting from all over the globe - we sat with two awesome guys from Ireland, a couple from Wales and a few others from the UK (can't remember off the top of my head as it was a few years back). Everything about the experience was top notch, they give you a goodie bag of swag, and an ex United player comes and chats for a bit and then will actually engage the crowd - it was a player from the 80's and the name escapes me now but he was more than willing to have a beer and chat with you for a bit. Pretty sure they give you preferred car park spacing as well which is nice especially after the game.
It's going to be cold and rainy in February and a game against Fulham is not going to be the most raucous crowd (my game was against Villa and I had a rant about it how the United posh fans were quiet af while the traveling supporters were in much better voice even though they lost).
I'm sure the additional value I got out of it was the booze and the people I was sat with as it was a fun fun pregame whereas the game was rather drab, but I did figured I'd be remiss by not throwing that out there to a fan. FWIW, the VIP package tickets go for well more than 2x what the Fulham game tickets were against a higher profile club, so you're getting a fair price, imho, especially for a stadium you may well never go to again.