A few questions about SSL :)

In webmaster tools you'll need to add your SSL site as a separate site. It's silly, but that's the way Google recommends to do it. You can't have both the http and https URL attached to the same property. You'll also want the www.domain.com and domain.com versions in there as well. It's a PITA. I have four properties for one website.

In wordpress you can install plugin: Really Simple SSL
next: Better Search Replace - this can change links in your database
in case you can install Velvet Blues Update URLs - this works like better search replace

done
don't forget doing backup after you do this