Is Xbox Live & EA Sports Server still supported on the Xbox 360?

Live is still supported. Not all of EA's servers are still running though. They have a list of all games that the servers are shut down for. https://www.ea.com/legal/service-updates

That doesn't sound like an issue Xbox Live Support has any control over. If I'm not mistaken, that's EA's age restriction imposed on their online servers. Users between the age of 13 and 18 may encounter this message when trying to access online servers
in EA games, or custom content. EA Sports games in particular require the user to be 18. This is regardless of your Xbox Live parental controls. Personally, I don't think companies should be able to override parents, but it is what it is.

Well, any kind of hack of modding is forbidden by XBOX LIVE Terms, but is EA Sports the ones who are in charge to ban from their servers the players who do that kind of hacks, and Xbox LIVE is the one who can ban the user from the LIVE online system only.

Sports games have licensing agreements, perhaps the licencing for FN Champion is different to FN4? Anyway, it's Not MS's decision to release, it's EA's.

If the Multiplayer still works on the Xbox 360, it will work on the Xbox One as well.

Actually, judge. I know quite a few people who play the older sports games because they see no point in spending 60.00 a year on nothing more than a roster update. It's also not just Sports games effected. I mean I was still an Avid Modern Combat player
when they shut those servers down and if I paid for the game, I should not have a time limit for how long I can play it. Meanwhile I can still play the launch game COD2 with no problems. I mean I'm paying for Xbox Live. Not EA servers and if they can't keep
support going, their games should be P2P or at least have a P2P option.