~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.
Sounds to me that you have covered all the bases. Maybe you should pay attention to few details:
Connecting old and new concrete; you have mentioned that you plan to do it, make sure that they are well stuck inside of old concrete (you drill slightly smaller hole than bar and hit the bar it with hammer when placed inside a hole. Also, you can chip old concrete (inch or two) so it will connect better with new one.
When it comes to posts I haven't seen the picture so it's hard to tell, but if you want to separate it from slab, you can do it by placing thin Styrofoam around posts before pouring concrete. Later on you can leave it or take it out and put some commercial products (make sure that those are for outdoor usage).
When it comes to changing the slope I really don’t see why would you do it? Accept if you don't like it. Anyway, if it's not causing any problems my advice is not play with it....I’m not sure it can be done properly.
Best Answer
Without seeing a photo of the scene I'd assume that you can put temporary legs in place. I'd install appropriate lumber at a slight angle to just outside of the patio area so that you can work on it unobstructed.
Plan view:
Place large blocks under the posts to prevent them from sinking into the soil.
Drive large steel or lumber stakes into the ground to anchor the temporary post legs.
Anchor the tops of the posts to the beams such that they won't slip out. This could involve lapped lumber scabs screwed to the posts and the beam.
Raise the beam slightly from its original position to allow easier installation of the new posts.
Block all access to the deck while the project is underway. Check the security of the temporary posts frequently. A collapse could kill.
How you repair or replace your patio is your prerogative. That part of the question is off-topic as either too subjective or unclear, given the few details you've provided about your ultimate goal.