Where is a good place for trekking in May?

My driving tips for Switzerland are to not drive. Switzerland is much better seen by train. Then you don't need to worry about speed limits, finding gas stations, navigating, parking, etc. Use SBB.ch/en -- you can get pretty much everywhere via public transportation better than with a car.

May is early for the mountains. Will you be ok with lower altitudes? I don't know the difference between hiking and trekking.

is this for the next couple of weeks or next year?

Next week!
I already make a reservation a rent car, because we are six people.

I want to see lush green meadows

You will certainly see that everywhere right now! It is only at higher elevations that it is still brown or snow covered. It will be green wherever you drive.

Since Switzerland has over 65,000km of marked hiking paths it would be helpful to know a bit more about what you are looking for.

What navigation apps do Swiss people use?

You can use Google maps here

I heard speed limits are strictly enforced — do you have any driving tips for Switzerland?

Yes they are! Always pay attention to your speed. Be sure you are familiar with how to navigate roundabouts. Watch out for cyclists. Know the rules for mountain roads - what to do if you meet a Postbus, etc. - since mountain roads can be very narrow, the bus needs the entire road to navigate curves. You must get out of their way!

Speed limits are strictly enforced and they can send you a ticket even after you return to the US. Your rental car agency will pass on the fine and an "admin fee" to you.