Re: Outdoor ceramic tiles?
What you're asking is to mud set the tile, & can be used outside, but it isn't generally recommended in freezing climates, which I think Detroit has.;)
The issue of how to treat the edges with exposed mortar is a problem too.
Any slabs or surfaces outside should always have a slope. An 1/8 or 1/4" per foot works well.
Possibly another slab could be poured on top of the existing slab & provided a pitch for drainage. However if it's not done properly & thick enough, it will crack. And then there's the issue of the slab settling. It may still be sinking.
I have no experience with mud jacking and have heard good & bad.
Ultimately the solution may be to remove the existing slab & replace it. If this is done, be sure to support the edge of the slab at the building so it doesn't settle. This can be done by bolting a steel angle to the foundation wall or by turning down the slab to the footing. The latter may be difficult since your frost line is at least 3 feet down.
By the way, this is a common problem because it is difficult to compact the backfill against the building properly. The solution is to provide some sort of ledge or foundation for the slab to rest on.