I have a Nissan Altima 2000 which I bought a couple of months back with 122500 miles on it.
Some days ago there was no Antifreeze /coolant in the car ( I had checked the Coolant box and the Radiator both were empty or there was hardly any coolant) and hence it will not leak or the coolant will not come out.

Recently I filled my Car Antifreeze box with Coolant fluid Prestone® 50/50 Antifreeze/Coolant and also filled some coolant in the Radiator directly.
2 days back I got my oil changed at Firestone and I was alarmed that the coolant is leeking from radiator along the Seams 431459 RADIATOR
(sides or radiator tap) actually there were few green spots.

So my question is "yesterday i went out and drove around 20 odd miles and there were vapours coming out from radiator as the antifreeze was spilled over the Engine and SEAM's of radiator, antifreeze was dark Green in color when i opened the Radiator cap which was very light in color when i initially filled it.

so is it normal or i need to do some thing."

According to firestone I need to change my

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SYSTEM FAILURE - REQUIRED
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CAPS : GAS, OIL AND RADIATOR
LEAKS ALONG SEAM
431459 RADIATOR
REMOVE AND REPLACE RADIATOR

324$
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PREVENTIVE MAINTENANCE - SUGGESTED
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RADIATOR CAPS
33028 RADIATOR CAP

COOLING SYSTEM
22515 UPPER RADIATOR HOSE
20795 LOWER RADIATOR HOSE
REMOVE AND REPLACE RADIATOR HOSE

THERMOSTAT
USE SILICON SEALER
REMOVE AND REPLACE THERMOSTAT

307$
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SCHEDULED MAINTENANCE SUGGESTED
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COOLANT FLUSH WITH SEALER AND CONDITIONER
95$
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PLEASE SUGGEST?

If your radiator is leaking, you will certainly need to replace it.
Often times, while the system is already opened, the cautious and more experienced shops will recommend a new cap and a thermostat, for sure.
And since the vehicle has ample miles and an unknown serivce history, a complete flush. That is something that can wait but that's up to you.
Get these repairs done and assess for needs after.

How are your vehicle's lights? Drive belts? Wipers?
Have you checked your tire pressures lately? Tread?
Winter's coming FAST! Don't get caught out in the COLD!

You can also take it to a rad shop and they can resolder the rad which can save some money. Your upper and lower hoses don't have to be replaced unless there is a problem. Sqeeze them and check for soft spots. Changing your oil and thermostat won't stop the leaking so unless you need to I wouldn't worry about it. Your car isn't new so there will be discoloration from how the coolant is now and how it looked when you put it in. Once they do the rad they'll have to put in new fluid anyway so you'll be fine that way for a while.