I mean, is there any type of evidence that Vikings used some kind of protective gloves to prevent enemies from hurting their bare hands holding the sword/axe or some kind of greaves (like the ones greek hoplites had) to protect their legs below the shield?
I'm sorry for my mediocore English, it's not my first language :)
I am a medieval re-enactor and have only studied history as a hobby, but I've got some possible answers.
It's likely that the hand grips of shields and swords were wrapped in something, probably leather. If you look at some swords from that period, like on this page, you'll notice that the grips are quite thin, to accommodate the wrapping.
A hand behind a shield is already pretty well protected from strikes, and you'll notice that those swords have a crossguard. That bit protects the hand as well, although of course, if you're struck right on the back of the hand or across the fingers, it won't do much.
A long shield also protects your legs quite well. In the Bayeux Tapestry, you can see some really long kite shields.
You don't see many gloves or greaves in early medieval depictions of armour, and even in later periods, lightly-armoured infantry would usually go gloveless and greave-less due to the cost of armour. In the Bayeux Tapestry, people seem to have bare hands and be wearing wrappings on their legs. However, mail gloves and greaves are possible back then, and by the 13th century, knights are wearing full chain mail onesies.
A maile haubergon could be made long enough to cover the knees, which are a hard to hit and mobile target anyway. The same can be said of hands if they're covered with maile "mittons" or behind a shield boss.
Also, your English is sublime and better than some Englishmen I've met, so no worries there! :)
http://i.imgur.com/tMsnXc7.png I made you a little drawing for your comprehension.
As you can see the max reach of a weapon is if you hold it horizontal to the ground at shoulder height. Then the farther your get from that position, the shorter your reach gets.
This drawing makes it pretty clear that the legs are not really the body parts most at risk as trying to lunge at your enemy's legs would have been a pretty risky move forcing you to overextend, causing your own demise if your enemy is not stupid. Add to that that the legs are pretty much always in movement and you will understand that protection wise greaves are not really the footman's priority. It is much better for a footman fighting in loose formation to have nothing hampering the leg movement, allowing him to run more easily and be more mobile.
