These answers are mostly dealing with basic combat mechanics and CONCORD. Once you get the hang of the interface and understand how to fit ships, combat in EVE Online starts to get much simpler.
Is it better to tank damage with shields or armor?
Shields use middle slots that could be used for many other things. They are also painfully vulnerable to EM damage, a relatively common damage type. On the other hand, they do not slow you down as an armor tank would. I wouldn't want to use a tech one shield-tanking ship against a Blood Raider NPC, nor an experienced PvPer that has had time to load an optimal ammo type. The passive regeneration of shields is pretty good for running missions, though, especially on the ubiquitous drake battlecruiser.
Armor is heavy and vulnerable to explosive damage (like that used by the Angel Cartel NPCs), but tanking with armor uses low slots. While shield tanking is usually a trade-off between utility and tank, armor is almost always a trade off between damage output and tank. Some of the ships that can armor tank end up having really intense tanks, especially against NPCs.
Is it all right to pod someone in high-sec if you are at war with them?
Yes. A declaration of war is total: CONCORD will stay out of it. You'd be surprised how many people assume that podding is not permitted, though, and let pods escape.
Will the NPC sentry guns found throughout low-sec get involved if player shoot at a war target?
Nope. War targets can fight in low-sec just as easily as they can in high-sec.
Can players fight other members of their corporation for fun, or does CONCORD intervene?
So long as you and your friend are in a player-run corporation, you will be able to fight without worrying about CONCORD. Note that all players begin in an NPC corporation and will return to one if they leave a player corporation without joining another.
EVE Online mechanic has a tragicomic side effect in that it is sometimes used by griefers and scammers. These players will join a player corporation, attend a mining op or other event, then attack and destroy their unprepared allies.
If players attack someone that stole from them, can anybody else get involved?
Assuming you are a member of a player-run corporation and not an NPC corporation, any member of your corporation can assist you. There is also a limited role that neutral characters can play by remotely repairing shields and armor. Otherwise it's just you two.
How can players avoid getting suicide ganked?
Step one: avoid attention. Don't run missions in Motsu, don't autopilot through Uedema, and don't taunt random strangers. Step two: don't be a victim. You shouldn't carry more than 100mil ISK worth of goods in an industrial, shouldn't fly really flashy ships like a navy raven, and should always have some kind of tank (even on mining vessels). Step three: stay safe. You should avoid spending too much time in .5 or .6 security status systems.