Is it safe to charge a MacBook Air after the green LED shows? Is it safe to charge my macbook after the green light shows? Would it not overcharge the battery, or reduce its lifespan?

I've heard that doing this is completely safe and it increases the cycles or something. Is that correct?
Is it safe to leave in?  Yes.  To understand this better we need to know what is happening when you have your charger plugged in.
What do the LED's on the MagSafe Charger Mean?
Amber:  Battery is charging.
Green:  Battery is fully fully charged and no power is being sent to the battery.
Your battery will naturally dissipate it's charge without use and the charger will detect this drop and automatically begin its recharge cycle.
Is it safe?
I am assuming you are referring to the longevity of the battery and not whether you will incur some sort of injury.
What affects the life of a battery are two things:

Number of Cycles - how many times the battery has been discharged and recharged.  1 cycle is a 100% discharge and recharge, or 5 20% discharges and recharges or 100 1% discharges and recharges.
Age -  this is actually the number one reason for batteries to fail.  Basically, a 3 year old battery that has never been used is going to perform about as well as a 3 year old battery that is used every day.

I answered a similar question recently about What's the best way to prolong the lifespan of a MacBook Pro battery?
Catalina Battery Health Management Feature
As of Catalina (10.15.5), there is a new feature; it's called Battery Health Management.  It will actually stop charging your battery and lower the maximum charge amount further making the micromanagement of your battery unnecessary. See the linked post for further details.
Leaving it plugged in will surely have pretty much zero effect on your battery.