If I'm understanding the problem correctly, switch the table from "Stay on Page" to "Move with Text" so that it can break and spread onto page 2+.
Since it is overlapping page header & footer, adjust Document margins to be greater than where you have header & footer positioned...
As you can see, top & bottom margin is set to 1 inch while header & footer is placed at .5 inch. This means the space for page content is INSIDE of the header & footer. Now you could have a thousand row table over many pages and none of them will overlap header & footer.
If you set the table to "stay on page" there isn't a latter page for it to flow onto. Instead, it's like it is BEHIND the next page, no longer respecting the document margin because it's like a very long table is laying on top of page 1 and flowing off the bottom. Then page 2 is laying on top of that (table). Switch my table example in the screenshot above to "stay on page" but leaving everything else the same yields the footer overlap (which is what I think you are experiencing)...
So switching the table back to "move with text" and adjust page margins to be
INSIDE of header & footer positioning should allow a long table to split and roll onto subsequent pages while respecting (blank) header & footer areas)... which is what I think you want.
And I think the "Something above the table" (jumps to subsequent pages) problem is that you have what is called a "Header Row" at the top of the table, which will appear on subsequent pages in Pages...
The idea being that information you put in a header row rolls onto the next page(s) so that people looking at subsequent pages know what each column represents. If you see numbers above zero in headers & footer in the "table" tab, you have header rows and/or header columns.
If you do NOT want these table headers on every page, you can create tables without header rows or, if you've already created a table like this, click the "1" to select the entire Header row, right click, "delete row" OR change the "1" selections in the table tab to 0 and the headers will become normal table rows and/or column. Then, they will NOT "copy" to the top or far left of each subsequent page.