Do I go to a bridal shower?

If the bridal shower is local, yeah you totally should go, if its some place you have to travel more than like an hour and a half to get to then send a gift, just becuase you cannot make it to the wedding doesnt mean you shouldnt show support.

It's customary to invite people to the shower even if you know they aren't able to attend the wedding. It gives the guests a chance to celebrate with the bride even if they can't make the trip to HI. There's no law that says you have to attend the shower or send a shower gift, so only attend if you think you will have a good time with other guests that day. But since you were invited to the wedding, you should also send a small gift even though you're not attending. I know it sounds dumb but that's etiquette.

Weather you go to the wedding or not is irrelavent. If your invited to the shower and am able to attend you should go. And yes buy a gift its no excuse to be cheap just cause you can't make it to Hawaii.

If you aren't going to the wedding, there's no point in going to the shower. To be nice though, get a minimally priced gift (put some thought in it) and send it to her. That way, next time you see her, it won't be awkward.

That's up to you. I have no idea how close you are to her. I only attend showers of those I am close to

It's up to you.