All your flights are Lufthansa flights you write.
If you bought them in one buy, they are one single ticket and the airline usually checks your luggage through.
If you bought them as separate tickets you might be able to have your luggage checked through, as they are all of one airline, even when done different companies do the actual service, just ask when you arrive to drop off your luggage. Or if you want to be sure before you fly, contact the airline and ask. Most airlines have e-mail and social media contact details on their websites.
When arriving in Geneva you will have to go through immigration and that will take time, with your luggage checked through there will not be a problem. But if you need to go out of the secure area, get your luggage, go through customs, go round to luggage drop off and through security, you may be very short on time. Leaving an airport can take anything from 30 minutes to two hours, depending on how busy the airport is. And there is little you can do to guess what it will be and it is also hard to go faster if you are stuck behind a long line at immigration.
Your stop at Zurich will be about the same in reverse, you leave the Schengen zone and will get a passport check, in which you should get a stamp in your passport.
If going out of the airport you can just walk out of the secure zone, pick up your luggage and walk through customs (if there, I am not sure.)
Then you need to check in your luggage, go through the exit passport control, which can take a while as you have to use one of the 'all other passport' lines, and go through security.
I think 3 hours should be enough but it might be tight when your arriving plane is delayed.
