Create Static Block
Goto CMS --> Static Blocks, and create new static block.
HTML code to display categories. Do not forget to replace each "ID" with the ID of the subcategory.
More info: Templates for display categories »
How to insert Static Block into the category page
Go to Catalog - Manage Categories and change display settings
Q: How can I change how many products it should show in this static block?
You can create a separate category for this static block and add products to it. They must be inactive to be hidden in the main navigation. Do not forget to replace each "ID" with the ID of the hidden subcategory. And how many products are there in the hidden subcategory - as many displays in the static block.