I'm not sure what you're doing wrong with that, but did you know you absolutely can have a long table on multiple pages? That itself doesn't seem to be a thing that needs to be solved or changed. I'd simply choose Repeat Header Rows (Layout tab, towards the right) so that your headers repeat at the top. And you can highlight your content rows, and under Layout/Properties, go to the Rows section of the pop-up, and de-select "Allow row to break across pages" if your cells are splitting across pages. You can use paragraph controls (Home tab, Paragraph section, Line and Page Breaks tab) to select "keep with next" and "keep lines together" if you have nested table rows.

You can also split the table - but where is your cursor when you hit Split Table? Typically you want to be on the row that will be the first row of the second table, not the last row of the first table. I'm not sure why rows are merging. Would have to see an example. You'll have to make a new set of headers if you split them into two.

Are you sure you're hitting Split Table and not Split Cells?

- Ann