Tile – How to smooth patio concrete for tile while maintaining slope

I would experiment a bit using some cutoffs and a steel combination ruler. Try to figure the average float percentage, I would expect 10-30% of the notch height for tiles that large.

The depth of mud under tile is variable, mostly based on the wall flatness and somewhat based on tile size. You have to float enough to bridge and give full support, more so with a natural stone tile like travertine.

Your edge profile will look best and protect best if its as flat to the wall as possible.

~Is the fact that clay is rocky going to cause any problems? I have removed as many rocks as I can but it is impossible to remove them all.

The rocks should not pose an issue as long as the soil base is compacted.

Can the depth of my crushed stone base fluctuate so long as it is always at least 4" deep? After excavating and removing stones the soil bed is not a consistent depth- some areas have space for 4" of crushed stone but some areas could go as high as 8" or maybe even 12" of crushed stone. Is this ok? Does it matter if the soil bed is not perfectly even so long as it is compacted, has geotextile fabric over it, and the crushed stone is lever after installation?

The geotextile fabric is good to use as a base over the soil base. Being in New England, you will see cold winters with the possibility of frost heaving. Thicker crushed stone bases help prevent this. 4" is the minimum crushed stone you will see recommended. If possible, increase that to a minimum of 6" across the entire patio area. When laying thicker crushed stone bases, it is good to use a plate compactor with every couple inches (3" or so) of base. With 4" of base, the plate compactor can be used once it is all laid down. With 6" or more it should be used two or more times.

Also, extend the crushed stone base at least 6" outside of the area to be covered by pavers. This will ensure the pavers stay supported by the crushed stone even with expansion and contraction.

The fluctuating depth should be minimized as much as possible, but it will not ruin your patio as long as the base soil is compacted.

~My last questions are about drainage. The patio will slope down 4" away from the house over 16 feet, which I believe is a good slope?

Yes. That's fine. 1/4" vertical drop per horizontal linear foot is a commonly accepted slope for drainage.

~Lastly, the water will drain right towards my detached garage (an old 2-horse carriage house that isn't nearly as nice as that may sound), which has a concrete slab floor and no foundation. There will be about 12" between the end of the patio and the garage. My plan is to dig a canal here to collect the water and move to another part of the yard to drain. Is this a good idea or am I asking for trouble having the canal so close to the garage? The setup of my yard makes it nearly impossible to have it drain in any other direction.

A concern with the patio being so close to the garage is waterflow from the patio causing erosion and undercutting the garage's slab foundation. I would suggest installing a French drain to divert water down this path rather than an open canal. The French drain would use 4" perforated corrugated pipe with a sock buried at least 4" under the surface. The pipe should slope at least 1/4" vertical drop per 1 horizontal linear foot, the same as the patio. Cover the pipe with 4" of pea gravel and top it with larger rocks, such as river stones. The rocks will help to break up and slow the flow of water to prevent erosion of the surrounding soil. The French drain will help remove water quickly to keep the soil from becoming water logged.

If you don't have an appropriate place to locate the exit of the French drain, you can dig a dry well. It is essentially a large pit filled with gravel into which the French drain can deposit water to be absorbed by the surrounding soil.