Excel borders are there but not shown on print preview and won’t be printed

Try publishing as (or printing to) a PDF file and then set the greyscale and one-sided settings when printing the PDF.

I don't think Excel can do that. A possible work-around is to use Microsoft Word and snake the columns around: How to snake columns to use fewer pages

Using MS Word to Snake Columns (#msword)

This is probably the easiest to use for a one time usage, since I've not put in a dialog into my Excel macro described later.

1. Select and copy columns from Excel spreadsheet.
2. Paste into Word, this takes a few moments
3. Select the rows to be repeated at top in the table, then indicate this in Word with Table --> Rows to repeated
4. Select entire table using anchor, or selecting cell(s) in the table and then Table --> Select --> Table
5. Indicate number of rows using the columns button, or Format --> Columns if you want more control over placement

This example works well. The post offers other possibilities, too.