Q: How do I flag products to appear on my home page? I've flagged one product to be a member of one of these categories, but it doesn’t show up in the box on the home page.
A: For products in the home page, you should create separate categories for each section and add products to it.
Q: On my home page should appear 10 or 15 products and always appears 9!
A: Please navigate to System->Configuration->Catalog -> Catalog Tab and change "Products per Page on Grid Default Value"