2 quick questions…

Hey all, just needed two things to be sorted out.

1. How would I add a form, for example, a ‘contact me’ form on to a page (not a category or blog post) on my WordPress blog/site?

2. I want to add the number of posts in the category next to the category headings. How would I go about doing it?

Thanks in advance, and I look forward to your help.