I recently attended a talk given by a Viking arms researcher at the Higgins Armory Museum (now sadly closed), so I can speak to some of your questions, though not the tactical ones.

Swords were definitely not reserved for the wealthy. Although they were costly items which required significant knowledge, labor, and time to make, the average Viking warrior would probably own a sword (though those of the wealthy would be better-made and much fancier).

For the Vikings, spears were quite common, but were used more by the lower class. They were much simpler to make, required less and lower-quality steel, needed less skill to use, etc. So your average Björn would have a spear, maybe an axe, but someone with a bit more status who was doing a lot of fighting would probably be using a sword.

Viking shield usage was rather different from what one might assume (at least, according to this researcher). Their shields were actually quite thin, a quarter inch of wood or less, which is necessary in order to keep them from being too heavy to be usable (as they are rather large). This means that a reasonably strong frontal blow can break through them without much trouble, so holding one in front of oneself for defense is a poor strategy. Rather, a Viking in single combat would have held his shield edge-on to his opponent, using it to deflect rather than absorb blows, and also striking with the leading edge. In formation, they sometimes formed a shieldwall, which requires a relatively large shield to cover both yourself and the man next to you, and the round shield serves this purpose. Basically, the round shield works better for their fighting style, as opposed to the rectangular shields of the Romans or teardrop-shaped shields of later continental Europeans, which had a different tactical purpose.

Chainmail was indeed both expensive and requiring of a lot of skilled labor, so something like a full mail hauberk would have been relatively rare- something only a higher-status man would wear. A more common sight would have been a mail coif or an aventail, which is a skirt of mail descending from a solid iron cap to protect the neck. Still not a cheap or common item, but far more widespread than full body armor.

Unfortunately, the tactical questions fall outside my knowledge- hopefully someone else will have an answer.