Yes if you migrate from a Mojang account to a Microsoft account you will receive the special migration cape
Do you roughly know the specs of your pc? The problem may be the video settings may be incompatible for your pc specs. You should try to go to settings and lower the render distance and disable some of the fancy graphics options and see if it helps the performance of the game first.
Unfortunately the migration cape is only for people migrating to a Microsoft account from a Mojang account. If you created your account using a Microsoft account you will unfortunately not get the migration cape
On your realm do you use a lot of command blocks or mob spawners?
It seems as now the problem has been fixed
There are 2 ways to fix this. First, you can connect to a wifi connection and that should let you play fine. The second way is to go to the settings on Minecraft and go to the profile tab and select use cellular data and that should fix it but I will warn you playing on cellular data will use up a lot of data and could lead to data charges. Also, you may experience lag depending on how good your service strength is. Hope this helps.
Disconnection issues are usually due to a poor internet connection on either the host (friend) of the server or the client (you). I would try to restart your internet router. If this doesn't work try signing into an Xbox Live account as this may prevent you from playing multiplayer games. Let me know if this helps.
I have been having similar issues with this server. It has a lot of bugs and glitches and a lot of lag/connection issues. I think your best bet is to just wait for a few days and see if they fix it. If they don't I would try to contact an admin on the server they might give you a refund but that's just my best guess.
Glad to here it’s working better