I want to have my blog setup as follows:

Remove pagination links on homepage (as simple as removing the Previous and Next links from the main page template, that is the easy part)

I also want to remove pagination all together from the category pages. Meaning When someone clicks on Category 1 it will list every article under that category with no pagination. Same for Category 2 etc etc.

Bump

Hmm not a clue.. try single.php

Negative. It's archive.php that presents the pagination links but just removing them doesn't remove the limit of 10 per page.