Hi WindyCityInsight and welcome to the forums
1)The Honda CVT has been around since its debut in a VX Civic in 94 (

) compaired to a 5 speed it has more parts to "break" (in general such is the case for all MT - AT compairsons). With that in mind it can be expected to have a shorter service life. However, few problems have been reported over the _years_ with them. In theory such complex assemblies are more susceptible to lack of maintenance. Genuine Honda CVT fluid and a 30K change interval are your best defense.
2) The IMA _battery_ waranty ONLY has been extended for this model. Unless the car has previously been "totaled." If its already been replaced its still unclear whether or not the balance of the warranty extension applies _or_ the replacement warranty. IIRC 12/12 (standard Honda warranty on all repair work).
3) Rain and snow handling is comperable to any other small car. However, the Insights relative low ground clearance will make curbing deep snow problematic. There are underbody aerodynaimc panels that can become clogged with snow / slush and damaged. Like all cars in the snow belt much can be gained with snow tires.
4). Depends on whether or not you need / choose batteries only or the improved controllers (MCM & BCM) and local labor rates. Low end for batteries only expect $2,500 +-. With 2 controllers $6,000

ouch

If its your nickel Re: the controllers they should be optional. You would be choosing to give up better control algorithms that are capable of further IMA battery service life extension. But so far there have been no reports of such being done.
Unfortunately the biggest factor in choosing a used hybrid is the remaining service life of the batteries. While they will ultimately more than pay for themselves in fuel savings a second owner must guard against loosing too much of the "pay back".
And before you ask there is no way to even reasonably "ballpark" the reamining service life of these batteries. Yes it could be done, but would _require_ some high tech and accurate gear not available as a "special tool".
HTH!