I think you have it pretty well sorted out! Just a couple of comments on your post:
In reply to:
About Gallery, do you think that just upload my gallery directory onto DH ftp will work? 'Cause I think there isn't any «export&import» procedure like the one from WP.
It might work, but there might be version (PHP and MySQL) issues that could prevent it from being that simple. Note that you will also have to move your Galley MySQL database to Dreamhost. Even absent any "established procedure", exporting your existing Gallery database from your current host, and importing it into a newly created DH database should not be that difficult. The Gallery forums should give you lots of help with any version/dependency issues and all that.
In reply to:
So, what I have to do now is to subscribe the L1 plan I choose and select the third option («already own a domain, I want to host it AND transfer the registration for free!»). Will it work even with my current hosting provider's DNS (as of now, we ALL know I can't change those!)?
I think that is the way to go (don't forget that deansfurniture already provided you with a custom promo code to make *both* those domains "free for the life of your hosting account" at DH *and* a cash discount - that's a great deal!). The xfer process should work with your current hosting provider just fine (they have to follow ICANN rules!), but make sure that you:
1) Unlock the domains at your current host/registrar so that they can be transferred
2) Determine what ECC or "authorization codes" you need to facilitate the transfer.
That done, you should be "good to go". Good luck and Welcome to Dreamhost.
--rlparker