Can I play splitscreen on Servers?

Unless there’s been a change recently no it’s not possible me and my little brother tried and I cant find anything that says otherwise so as far as I’m concerned no, you can not.

Well it doesn't work just like that out of the box, however if you are a little techy and you feel like you can install windows there is a trick, assuming you are going to do this on PC. The keyword for this is called virtual machines. They are used pretty much everywhere, but most commonly on huge enterprise servers. You can try it out by installing virtual box. When setting up a virtual machine make sure it gets sufficient RAM, CPU and video mem.

Now to the controller issue: they really have to be 2 separate devices. Either wired, or you need 2 separate wireless receivers. It is then possible to map one device to one machine and the other to the other one. By running 2 virtual machines, you can get something like a split screen.

This is the only way I can think of, having multiple minecraft screens with 2 separate controllers on PC.

I really hope this could be somewhat helpful, and have fun tinkering, in case you decide to tackle it.