If there is moisture still there, then mold and mildew will return. If the problem was not fixed, then it will return. Bathrooms are particularly bad in this respect, since moisture is a natural consequence of using water. I would expect to need to redo things like caulking every few years to fix this. It will not last forever.
Scrape/pull off the old silicon.
Apply a solution of bleach to kill the mold. Be careful when you apply it, as bleach can damage the clothes you are wearing. Keep the area ventilated well.
Let it dry. If you are in a hurry, a fan blowing on the area will help. A hair dryer can also speed that process considerably.
Apply new caulk in a smooth bead. I use my finger to spread it along the joint. Definitely use a high quality silicon caulk with a mold/mildew inhibitor. These are caulks that are designated for use in bathrooms.
Allow it to fully dry before you get it wet again. Give it a day or so. It will skin over in an hour or so, but make sure it has properly cured before use of the shower.
Expect to redo this process in some number of years. The exact time it will last depends on how well the area is ventilated.
Of course, there may be mold in the wall itself. This is difficult to deal with unless you tear the wall down to replace it completely, and even then water tends to attract the stuff. Mold spores are everywhere.
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 think your "slurry mix" is a floor leveler? Is that corect? Your pouring a slurry to level the floor. That would be the correct procedure to prepare a rough surface for tile
After it hardens tile installation can begin. You want to use a thin set adhesive to bond the tile to the surface. Thin set is mixed with water and /or an acrylic admixture (for resiliency) than troweled (notched). Tiles are pressed and set accordingly. Wipe away any squeezed-out thin set with a damp sponge.
When troweling grout into joints do so at a 45 degree angle to the tile joint. work 3' x 3' areas (or whatever is comfortable). Wait for the grout to stiffen or when you wipe a moistened sponge across the grout joint it stays in place. Rinse frequently and wipe gently.
When you see a haze develop on the tile surface you need to wipe it with a dry rag or cheese cloth. Don't let it sit or it will be a real problem to remove.
That's the short answer on tile installation. It's more difficult than it looks and is best to have someone who's knowledgeable with installing it to be present.