1. Email
I tried adding email addresses by following your instructions on http://en.support.wordpress.com/domains/add-email/add-other-email/ but it doesn't seem to work. I sucessfully added all the neccessary addresses on my host but all the email I try to send still bounces.
I changed the custom DNS in the WP domain settings to
MX 10 MAIL.DREAMHOST.COM.
What could be the problem?

2. Privately hosted blog limitations
Just to check if I got this right.

You can move your WordPress.com blog to a web host that allows editing and uploading of completely custom themes. You can find suitable hosts here.
(http://en.support.wordpress.com/themes/adding-new-themes/)

So this is what I want to do since I already bought a theme and realized afterwards you don't allow uploading custom themes to wordpress.com, but it seems that even that won't help since I would then have to map this domain to the new host, and:

The Domain Mapping Upgrade does not enable the permission to use advertising, any kind of prohibited code, or upload additional themes or plugins.

I got hosting at Dreamhost after seeing that it's possible to upload custom themes to the installed WP, but even when I got private hosting and installed WP.ORG on it, I cannot upload the custom theme because the domain is owned by WordPress?

And I cannot transfer the domain from WP since:

you may not transfer a domain name for 60 days after its purchase or registrant contact information change

?

Can you please confirm this or propose an alternative for solving my problem?

Thank you.