Wow, you've stepped into a quite complex subject..
I'll try to help you as well as I can..
1) RoHS can be self-certified, and that is indeed how most companies do it. I.e, if you're sure you're RoHS compliant, you need to produce a "Self declaration" document that specifies that you've either measured or know about the substances in all parts of the product, and that the 10 substances that the RoHS covers are either not present or below the threshold limits.
Example self-declarations:
http://www.hitachi-america.us/supportingdocs/forbus/inverters/Support/hitachi-self-declaration-for-rohs-compliance.pdfhttps://www.pickeringtest.com/content/pdf/rohs-60-102-103.pdf( Note: Both of these are older documents, and there are now 10 substances )
2) Yes, you need to consider WEE as well when selling a product in Europe. I'm not terribly familiar with WEE, though.
3) I don't know of an official RoHS logo. In fact, you're not required to even put the logo on your product. (RoHS is still required though. You still need to do the self-certification if you're selling in the EU)
Also, don't forget about CE markings. They're also commonly self-certified (unless your device doesn't fall under the Low-voltage directive, then people tend to prefer external test-houses).