How to switch input in split panel terminal

It's meant to be like that. See this Super User answer:

You're misinterpreting the feature. It's not meant for two separate terminals. It's intended to allow a user to see two different view points in the same terminal. For instance, if you have 3000 files in a directory, and you perform an ls command, that output is going to be very long.

If you use the split pane, you can scroll through that long output without having to flip back and forth, possibly losing your place along the way.

If you want two terminals, use tabs, or separate windows.

I would add that, for two separate terminals, you can use separate tabs as well.

cat xaa > newfile
cat xab >> newfile
cat xac >> newfile

Basically using a single '>' operand send the output to a new file. using a double '>>' operand makes it append the contents to the end of an existing file (and also out of interest create it if it does not already exist.

If all your files are definitely in a neat alphabetical order, then you could use:

cat x* > newfile

or

cat xaa xab xac > newfile

in case the filenames aren't in alphabetical order.