The reason that roasted garlic tastes so much milder than raw garlic is that it contains a sulfur compound called allicin, which roasting breaks down. Allicin is primarily what gives garlic its pungency. Technically, raw garlic mostly contains a compound called allin, which reacts with the allinase enzyme to produce the allicin, and this reaction is greatly accelerated when garlic is "distressed", i.e. crushed or cut.
Ginger contains no allicin, so you're certainly not going to get an identical reaction. What ginger does contain are two types of oil called gingerols and shogaols, which are primarily what gives ginger its pungency. Cooking converts these into another compound called zingerone, which is far less pungent (it's described as "spicy-sweet"). It's actually slightly more complicated; the gingerols also convert into shogaols through cooking, and the shogaols are actually more pungent (160,000 SHU vs. 60,000), but on the whole, the ginger does become milder.
It will not become perfectly sweet as garlic does, just less pungent and more aromatic. In fact, cooked (roasted) ginger tastes much like dried ginger; many of the same reactions happen during drying as during cooking.
So yes, you can try roasting ginger if you want it to be milder, but don't expect to be able to eat the whole root by itself if you don't already love the taste of ginger. It doesn't do exactly the same thing that garlic does, it's just a little similar.
It's hard to find good references online, although you can find a lot of this in McGee. For more information you can try:
Best Answer
If you have a lot or don't anticipate using it in the next 5 days, then freeze it. If it's already minced or pureed then simply measure it into quantities that will be the easiest for you to use and then freeze them on a tray lined with plastic wrap. Once frozen, remove and put into a self-sealing bag and keep in the freezer for future use.
Whole ginger can be frozen simply as it is. Just put it a bag in the freezer. Galangal for example, is commonly sold frozen in asian markets You can pull it out and grate what you need on a rasp style zester while frozen. I never even peel ginger as most uses for it require it to either be minced finely or strained out all together. A little gingerroot skin is just more fiber for the diet.