This looks like a mess (I know, I'm not telling you anything new). The grout haze isn't going to be easy to remove, but it can be done with an acidic grout haze remover. Because it has been there that long, figure on allowing the grout haze remover to sit on the surface for quite awhile. Try to keep it away from the grout where you want grout. It will require multiple applications and some elbow grease. Our product:
http://www.mapei.com/public/US/produ...ver_lr__EN.pdf
The best you're going to be able to do is to get a few years of use out of this shower before you'll have to rip it out and start over. The water is going to pool on the floor due to lack of slope and get behind and under the tiles where it will damage whatever is back there. If you're cool with that, you can grout the big grout joints with a product like our Ultracolor Plus that can go up to 1". I'll warn you ahead of time, it's going to crack because it's at the change of plane, but there isn't a flexible adhesive that is going to do much good here. Product info:
http://www.mapei.com/public/US/produ...lus_tds_ea.pdf
It's really up to you, if it's a cabin that won't be used often and you're OK with trying to stretch it until you can afford to do it right, there are products that can fill the gap and clean the tiles. If you're at a place where you can tear it out and have someone do it right, it would be a better choice.