(Don't have SHT15's)
I've never used DHT22's with cables longer than 1 feet. You probably need pullup resistors to improve the signal.
Can the DHT22's unique 1-wire-ish interface be daisy chained (like the Dallas 1-wire stuff)?
No, you need one wire per sensor (and two for GND and +5V but that can be shared), the Dallas thingies have an unique address. An UTP cable with 8 wires could in theory support 6 devices. => place the Arduino in the middle to minimize cable length?
Will the DHT22's accuracy remain constant or drift and will it be consistent across a variety of DHT22s?
I have two of them and I recall they were pretty close when I tested them (for DOA) when they arrived. Never did a range test.
Most important to know is that the DHT22 are relative slow. Think in the order of 1 sample per 2 seconds, and they take some time to recover.
Is there another temp/humidity sensor available that would work better without breaking the budget, perhaps a Dallas 1-wire sensor?
For temperature the Dallas DS18B20's are quite good. I'm not aware of a Dallas 1wire humidity sensor.
What does it take to weatherproof these for outdoor use?
You need a roof on a pole so rain (even with wind) cannot touch it, somethingh like
The S is the sensors
Are there other questions I should be asking of these sensors?
Do you expect the humidity
to be much different in the various locations? Do you really need 10 of them? I can imagine that 1 outside and maybe 2 inside (living & kitchen) may be enough. And use temperature-only for the other locations, as temperature may vary more than humidity (I assume)