You can send anyone really anything? If it is funny they may laugh. If it is expensive, they may send you a thank you card. If you expect anything in return for doing it? Good luck. When you send a b-card to a relative or friend, they may say thank you for the thought. If you don't know that person, they will probably forget about it. If it is a nice card, it may be something positive that they need at that moment?
Weird? Could be? Depends on the card. Presents? It's like giving to charity though I always appreciated a kind word or something good to eat, if I liked it? Lots of people say, "good job" or "nice performance". A gift, if it is useful to the person who receives it, can be nice? No one wants anything that comes with "strings" though. Especially from a stranger. So don't give anything you expect to be kept or sentimental. It might end up that way but I try to ask permission first before giving something away. If it is something that can be shared, I try to give it before the show. That way, if someone is on a diet, they won't feel guilty by not eating it.
I think looking up someone in the phone book,(who lists their numbers these days?), is pushing it. If they don't want to give out their home address personally? I don't think it is such a great idea? If you are in love with someone who doesn't know you and are hoping this act will win you points? Could go either way? If you send a picture, who is going to believe it is really you? If they are involved with someone, it could go very bad for either of you.
Most b-day cards end up in that great circular card file in the sky. If you really feel you just have to say Happy b-day, I don't think it's a problem. Unless you have been told don't send anything or they publicly state, this bothers them so much! It is all very personal and individuals all react differently. I think, if you keep sending stuff with no reply, it is pretty much a lost cause. They are probably too busy just trying to stay employed. Fanletters? That's different but many actors don't reply so that too may not generate the response you were hoping for.
The album thing? Wow, that must take some effort? I would really ask first? Unless you don't mind if it ends up, again, tossed away. It probably wouldn't even be personal, just housecleaning. So for most things beyond fanletters, I'd say only do it if you have the time and can face it probably won't gain a response from the person getting it. I think, if it makes you happy to feel like you are giving something back for all of their hard work on stage, how can that be such a bad thing? I won't condemn you for it. If your intentions are good, most appreciate being thought well of by anyone.