[Closed] Small terrace drainage issues and tiling

I know there are some good builders and DIY types on here so I have a question! My house is on a slope and the back door opens on to a tiled terrace about 2x6m. This is a brick and concrete construction and houses a small 1 story shed accessed from the level below. Left hand corner away from the house has a set of stairs down to next level, right hand corner away from the house has a drain feeding a drain pipe that handles run off from the terrace. However water pools on the tiles and is leaking into the shed. The terrace has a knee high brick wall and railings around the edge.

So the summer/dry weather project is to rip up the tiles (very weathered) and sort out the drainage. So what are the best ways to do this? I was thinking:

1. Remove tiles and clean out any damaged concrete and bricks
2. Fill any holes and try and sort out a sensible drop to the right hand corner. Tips and ideas on what to use and how to do are appreciated? Do you simply decide the drop you want and then mark out with string and then skim with concrete?
3. Seal with some kind of weather proofer? Or is liner better? Suggestions on what to use.
4. Lay suitable tiles with a appropriate exterior adhesive and grout. I assume flexible stuff is best?

I am reasonably capable (as in things tend to work but take a long time and might not be pretty!) at this sort of stuff but I am prone to starting before I really have a plan! So ideas and tips appreciated!