1. You can take the Malpensa Express train to Milano Centrale station and change to a regional train to Varenna.
2. Considering that the train trip is two one-hour legs plus unknown time between trains (maybe 15 minutes, maybe 2 hours) and you want to rent a car eventually, it might not be a bad idea to rent at the airport. Varenna is maybe one to two hours from the airport, depending on traffic, short cutting north of Milan.
3. See 2.

First, Milan has two airports. If you arrive at Malpensa, you take the train from there to Milano Stazione Centrale, then another train from Centrale to Varenna. Be careful: there is also a train from Malpensa to Milano Cadorna, which is NOT the one you want. A taxi from Malpensa to Milano Centrale is €90 (fixed rate), and doesn't save time over the train (which takes about 40 minutes). There are also buses from Malpensa to Milano Centrale, which are a bit cheaper and take about an hour. The train from Milano Centrale to Varenna takes about an hour.

If you land at Linate, there are buses to Milano Centrale, or you can take a taxi (only about €25, as it's much closer to the center than Malpensa).

If you take the train to Varenna, you will have to return to Milan to rent a car (you'll see why when you get to Varenna - it's a very small place). There are car rental offices at Milano Centrale, and that's the most logical place, rather than paying for a high speed train to Verona and then a car rental on the same day (the train from Varenna to Milan is a regional train and so is cheap). Or, as Sam says, you could rent a car at your arrival airport for the whole trip.

Thank so much Harold and Sam for your input...I appreciate it. I think I'll take your advise and rent a car in Milan from the start.

I agree with Harold. Rent a car directly at the airport; it'll be easier for you to continue your trip to the Dolomites.

From Varenna to the Dolomites take the alpine route. Longer but far more scenic.

Parking in Varenna is not easy.

Do you have reservations at one of the two big hotels? If not it is unlikely that your lodging will have parking. There is a multi story car park just down from the church - not cheap - (the car park not the church) or there may be parking on the road from Milano beyond the Cipressi. Park on one side of the road only, as close to the kerb as you can, an as close as possible to other cars to give the maximum number of cars a chance in the limited space.

1. Since you plan to rent a car after Varenna, just rent one at Malpensa airport (I presume that is the airport you will arrive at).
2. See above. Rent at airport.
3. See above. Rent at airport.

If you prefer not to have a car in Varenna, the best way is to go back by train to Lecco (southernmost tip of the Lecco branch of the lake). Lecco has rental car offices (for sure Europcar has an office). Then drive back up to Varenna, pick up the rest of the party and drive through the Stelvio pass into Merano-Bolzano-Dolomites (Val Gardena?). Merano is pretty and you should visit it or even spend a night. The path is Varenna > Sondrio > Tirano > Bormio > Stelvio pass > Merano > Bolzano > Ortisei (Val Gardena). The last is my suggestion, since I'm sure you'll like Ortisei. Then from there you can drive the Sella Pass into Canazei etc. Stay in Ortisei overnight.

PS: the road up to the Stelvio passes very close by the border with Switzerland. Stop the car for a sec, walk in the fields for a couple of steps, take a picture while in Switzerland then tell your friends you've been in Switz. too.