Should I invite someone to the wedding , even if I know they can't attend?

Yes, you should. If you don't you run the risk of them feeling as though you did not even think about them and hurting feelings.

So, etiquette says that invitations should go out to everyone you would like to attend, whether they can.

YES! Especially if you want a gift! Lol! ;)

Yes, out of respect for that person!

Yes, you invite that person. It is their choice to attend or not, to give a present or not. If you know there is a financial hardship for this person, offer to help out, if you can. When I got married I knew my one uncle would not be able to attend due to finances and I sent him the airline ticket. He was my Mother's only brother.

I will thrown this in, I got hurt when a close friend got married, he knew my job would not let me attend, but he did not give me the option of missing work ( I would not have but I should have had the choice)

He can not have a second chance to do that now.

Absolutely, you should invite those whoom you know cannot attend, the perk is that you will probably still get a gift.