Traveling to Cyprus through Geneva and Zurich

Assuming you are a US citizen and you are traveling on one plane ticket (i.e. not tickets bought separately):
1. You don't need to worry about this. Just follow directions to your next gate like you would at any airport; if immigration check is required, it will occur somewhere on the way to your gate; just stand in line a few minutes and get your passport stamped. Two hours is plenty of time.
2. Same answer as #1.
3. No visa needed for US citizens. See US Dept of State travel website for info.
4. Yes, you can leave the airport.
Enjoy your trip!

I find this a very strange route. Two changes to get to Cyprus! Most airports in Europe have flights to Cyprus, as it is a popular holiday destination.
Also flying from Geneva to Zürich is unusual, they are so close. It is only 3h10 by train, and there are 2 trains per hour. I am surprised there are flights between the two.

1) Normally you would not go via immigration, as Cyprus is not in the Schengen Area, but as you are taking an intra-Schengen Flight, you would have to enter Schengen at Geneva, and leave again at Zürich. I.e. immigration at both.
Assuming your bags are checked through to Cyprus, you will not see them until Larnaca, and after you pick them up you carry them through customs.

2) 3 hours - plenty.
3) Don't know. You don't say what nationality you are. The Cyprus Embassy site would be where to get a definative answer.
4) Yes and Yes. You can leave the airport, but if you do so you have to go through immigration to enter the Schengen Area, and again to leave.

It's all through one airline, so I figured it wasn't thatttt strange. Swiss Int on the incoming flight(s) and Lufthansa on the outbound flight(s). It's been pretty hard to find any direct flights from my spot in the USA to Cyprus (I'm going in the height of tourist season I believe, and all the flights had 2+ stops)

I am American, so it's looking like i'm pretty much exempt from any visa requirements.

So...I would arrive in Zurich, go through immigration/customs and be stamped into the Schengen zone...then when I go to my flight in Zurich, I will also go through customs and be stamped out?

So...I would arrive in Zurich, go through immigration/customs and be stamped into the Schengen zone...then when I go to my flight in Zurich, I will also go through customs and be stamped out?

I assume that is a typo for "I would arrive in Geneva".
Immigration is for people. That is where they decide if you are allowed into the country, if so for how long, and if necessary stamp your passport.
Customs is for goods. This is where they examine the contents of your luggage to see if it contains anything banned, or for which customs duties (taxes) are payable.

Landing at an airport (any airport), the following happens:
1) Disembark
2) You go through immigration (passport control)
3) Pick up your luggage
4) Carry luggage through customs
5) Exit through arrivals.

• Landing at Geneva, you go through immigration, entry stamp if US citizen. But your bags will presumably be labelled through to Larnaca, so you will not see them.
• Departing Zürich, you go through Immigration (exit stamp). There is never customs when departing.
• Landing at Larnaca, Cypriot immigration, pick up bags, Cypriot/EU customs. Customs is a "Walk through", they only stop a few people (<5%).