I can try to answer some of these. I have a 2003 Civic Hybrid, CVT, 41K miles. I love the car - haven't had a moment of regret, especially now with gas what it is.
Are HCH's reliable? Any common issues or problems? Any big things I should know about? I haven't had any trouble with mine. Standard maintenance checks, and they fixed a rattle in the dash. The recalled it once, only to upgrade the computer. I did get the extended warranty as a precaution.
How are HCH's in snowy/icey conditions? Where I live (CT) we can either get a bad winter or no snow at all so I need to be ready for a bad one. I'm not looking to get thru a foot of snow, but if there is like 3 inches can I make it home from the office? I don't run into much at all - someone else may have to weigh in.
How is the HCH on acceleration? Gets up hills okay? Enough power to pass on the highway? It gets around just fine. I've passed people going up hills before. With my CVT, response is not instantaneous, which is a bit of a change. You don't floor it and get that immediate down-shift and surge of speed. It does, just with a small delay while the engine and transmission figure out where they want to be. In all, it requires a bit more cautious driving style. I do a LOT less weaving in and out of traffic, which is actually a good thing. I'm actually a much safer driver in this car.
Gas Mileage, is it close to what the EPA estimates? If it's 40MPG its better than what I get now. Driven poorly (aggressively) folks get in the low 40's. Driven properly, you should get EPA. Driven well, you can get it into the low 50's. A lot of factors are at play - hwy vs city, weather, etc. My lifetime over 3 years is 45.6. Last three tanks have been 50, 48 and 52 - mostly due to change in how I drive.
Tax deductions, from my understanding there is a 2000 dollar tax deductions for 05 and I beleive the state of CT waives or refunds sales tax on Hybrids. Can anyone confirm this? Can't comment - mine was a 2K deduction in 03.
Is it hard to get used to driving a hybrid vehicle? I noticed the Accord shut down while stopping, Civic does the same? Not hard, but keep in mind to get the best mileage you'll need to change some of your driving habits (if they are aggressive, meaning fast starts, quick stops, etc.). You can't drive it hard and expect to get 50 MPG. The Civic does autostop like the Accord, under certain conditions. You'll get used to that. In fact, when we're in my wife's car it drives me crazy that the engine is on at stop lights.

The CVT took some getting used to as well. Nothing I didn't adjust to in the first couple weeks of owning one.
Is pricing available for the 06 HCH? I'd be buying an 06 prolly with nav and all. Don't know. The 06 looks nice...
If I had to summarize - expect a Civic. Decent options, reasonable transportation, excellent quality, great mileage. It's a bit lacking in "fun" factor, but what's fun for me now is going 550 miles on a tank of gas. I traded in an Infinity - I really don't miss it.
Good luck with your purchase!