If kept in its vacuum sealed package, even a bag of fresh oolong will last up to a year or more before it becomes noticeably stale. Once opened, it is best to drink it up within three months or so.
Dark, roasted or red oolongs (and red tea) can last much longer. Sealed, they keep pretty much indefinitely. Opened 150 gram bags, as long as they are clipped shut, should still be able to last for a couple years.
For a gongfu session, you'll probably used between 5-10 grams. For a grandpa session, 3 grams is usually enough. 
You can do the math yourself, but I use these general rules :
30 grams = Try it four or five times
60 grams = A couple sessions a week for a month
150 grams = A session most days for a month
The reason we use these vacuum sealed bags is because they are the best way we know of to keep tea fresh, opened or not. Once opened, you can push all the air out of the bag, roll up the top and clip with a standard binder clip. Generally better not to store in a jar or caddy because there will be more space at the top for air to get in.
There are exceptions as you get into advanced tea storage; a good caddy can really help open up an oolong tea.

 

When tea travels a far distance, especially by air, it has the tendency to go into shock. This will mellow out over the course of a couple weeks.

 

Sometimes a tea just needs time to acclimate to its new environment, regardless of distance traveled. It may need time to settle into your tea space, for example.
Roasting can also have the effect of making a tea feel 'bound up'. I.e. The flavor of the roast will take over the foreground. This will mellow out over time, sometimes very quickly and sometimes as long as a year.
We get this question a lot. In general, when re-steeping the same leaves we try to do it within one sitting. Brewing a couple infusions, walking away, then coming back to it can be fine, but won't give the best results. Also, in that case the tea will 'sweat', so be sure to shorten the first infusion time upon your return.

 

If you do take a long break between infusions, don't put it in the fridge. It's not going to spoil. If you don't come back to it within 24 hours, probably safer to dump it.
The short answer is we don't know, they are not tested. 

 

It is a commonly held belief that green tea has less caffeine than black. This has been proven untrue. Caffeine doesn't vary due to production method, but rather by growing conditions. And since all of our teas are grown in Taiwan, the amount of caffeine will not vary THAT much.
But how a human body reacts to caffeine from different types of tea can vary A LOT from person to person. For example, with green tea some feel more jittery, and with black tea some people can sleep directly after. Roasting does have an impact on caffeine content, but some of the strongest teas I've had in my life were roasted oolong.
This one is a bit of a non-answer. If you are looking for a hot beverage for the evening and you really can't do caffeine, I'd recommend keeping fully steeped out leaf from earlier sessions and reinfusing them one last time.
I've also found GABA is a pretty good option before bed.

 

No, you don't need one. All you need it a cup and hot water. See video below. (A good pot can however greatly expand your tea experiences)

Brewing Guidelines