If your tile is not secure, then the backer is not secure either. You will need to gut it to the studs and install water proof membrane, concrete board or heavy hardy-backer to tile over. The window frame must also be carefully water-proofed as well and trimmed out with a moisture resistant material. Get some professional advise on this one, a new tile job is not cheap or easy and be a shame to have a leaky, grout dropping job when you're done.
As far as the type of tile, ceramic or porcelain are similar products, difference being the hardness grade and the type of glazing. Porcelain is always a better choice in my view as the surface glaze is smoother, easier to keep clean and usually a harder grade.(3 to 7) prices can vary wildly, usually again because of the glazing and hardness factors. Designer patterns also effect the cost as well.
I'm very sorry to say this but you're going to have to remove all the tiles and start over. You will never been able to prevent this from leaking fully.
It may also mean removing and replacing the backing as well.
The critical step you missed was the waterproofing membrane that goes under the tiles and in and over the drain pipe. The tiles don't stop the water at all but are for aesthetics only (and to protect the water proofing). What makes the shower water tight is a sturdy backing covered with a water proofing membrane like liquid flash (one I used) when I did my tile shower. http://www.constructionchemicals.com.au/products/waterproofing-membranes/
But there are many different brands. They are a paint on product and very easy to install.
Don't expect your tiles to be waterproof. At best they are only splash resistant. Water goes right through the grout and can also enter around the side of the tile where the grout is. Porcelain tiles aren't quite as porous as ceramic, but most wall tiles are ceramic because they are a lot lighter. These tiles act like a wick and just draw the water through to the back of them. If you don't fix this you could be in for some serious mould issues down the track.
Unfortunately there is no simple fix to this but to start over. I would not recommend just trying to seal it. It's like covering up rotten wood with paint, it won't last and won't fix the problem long term. Although you've got water resistant plasterboard. It won't last long term. These plasterboards are just designed to repel water to keep it out of the gypsum they are made of, not designed to be constantly wet.
Interesting construction that your builder used water treated plasterboard + chipboard for the construction. 6mm or 1/4 in thick concrete based tile & slate underlay board + waterproofing membrane is all you would have needed. I wouldn't recommend tile on plasterboard at all. Even with the layers that he has. It's not as strong.
Since I know how much work goes into these DIY tile showers I will say this. If you feel overwhelmed, call in an expert. They will have the job done in a week and you'll be able to move on with life. But if you're up for the challenge and want to learn to do it right this time, then dive in and go for it!
Best Answer
I understand that you are just replacing the tile and leaving the bathtub. So, you should have no problem taking a bath in the tub at any time during the tiling. As far as a shower, you can be creative with some polyethylene plastic taped or draped around the three walls and take a shower too throughout the project.