I have yet to find a wonderful solution for hair washing, especially as they get older! When my girls were babies, I would wet their hair with a washcloth, and rinse it the same way, and everything was fine. But now, (at 20 months and almost 4 yrs.) they cry and try to get away the whole time. Not a whole lot of fun. I've tried having them sit up in the tub, lie down in the tub, hold a dry cloth over their eyes, in the shower, what ever. They just hate it! So we do it fast. My only tip for that would be to stay calm and gentle. If it seems like you are panicking too, it will make it worse for them!
About baths for the tiny ones - my babies both LOVED their bath if I was in with them. They would feel warm and secure resting on me, and then the bath was great. I think usually babies cry in the tub because they feel insecure. That's what the cloth on the tummy helps too - makes them feel like they are cuddled, a little bit.
And as far as showering with a baby goes, I haven't really tried it, but my sister does it all the time with her girls (2 yrs and 6 months) because they have no tub, and she doesn't trust them alone while she is showering! She fills up the baby tub with warm water and sets the little one in it on the floor of the shower, and makes sure the water isn't going to fall on her face, and lets the two year old just stand in the water with her. When everyone is done, you can get out, slip on a bathrobe, then get the little ones out. If your bathroom isn't too big, it will warm up from the shower, and they'll be fine.
HTH!