1) The invitation wasn't actually sent to "us" directly from the Happy Couple (HC), instead it was sent to DFi's parents and then on to us. The address except for the postal code is typed, it's obvious DFi's parents wrote it in. To me, if you're going to invite someone to your wedding, go online and find out their address. Yes, that part is tacky. You should hand address wedding invitations, and you should definitely find out the correct address of the invitation recipient.
2) The invitation was addressed to "Mr" DFi. DFi isn't a "Mr", he's a "Dr" - as he likes to say, he didn't go to Evil Graduate School to be called "Mr". His relative knows it's "Dr", it's on the invitation/information we sent them for our wedding. I'm not too sure about this one. To be honest, I'm not sure what the appropriate social etiquette is for people with Ph.D. degrees, not medical doctors.
3) The invitation was to "Mr DFi and guest". Aside from the fact that the etiquette mavens say that "and guest" isn't appropriate for a wedding (who knew) - DFi and I have been going out since 1998. We've been engaged since 2001. The relatives already have the invitation for our wedding and oddly enough that invitation has my name on it, so it's not as though they have no idea I exist. I've never met the relative (DFi's extended family is quite large) but still, they're perfectly aware that DFi is about to be married. According to my etiquette book (Emily Posts), the term and guest is acceptable. If the couple does not indicate and guest on a non-married persons invitation, then the invitee is not supposed to bring a guest. However, both members of an engaged couple are supposed to be invited to weddings according to etiquette. Additionally, if the name of the guest is known (and in this case it clearly was), then you should address the invitation to Dr. John Doe and Ms. Jane Smith if that makes sense.
4) Included with the invitation was a little mitfull of registry cards. I'm sorry, it's just tacky. I still think registering is tacky (even though I had to register for our wedding) but registering just isn't "done" here. Well it's starting to catch on, but it's nowhere near as prevalent as in the US. Registering isnt tacky, but including registry cards and/or any mention of gifts with the wedding invitation is tacky. Basically, it gives the impression that the bride and groom are looking for gifts. Now of course wedding etiquette dictates that wedding guests should bring gifts, but the bride and groom should never be seen as asking for them.
All that being said, don't let it bother you. Just send your regrets (since you mentioned you can't attend), and a gift.