Some newbie questions from me

You'll have to be a little more specific. What DG are you playing as, what build are you using, and what AI difficulty are you playing on? The hard and nightmare AI get buffs, which would make them level faster than you. But I'll try to answer as best as I can for now:

1) Killing creeps(the guys who spawn from the portals) is the best way to get experience early-game rather than killing other Demgods, as they seem to give you more. You can easily get to level 2 by capping a flag and killing one wave of creeps. Don't get me wrong, I'm not saying you shouldn't go for kills. I'm just saying that early-game you should focus on leveling up more.

2) There are items that can increase your autoattack(most of them are gloves, although artifacts do as well). The best way to increase your damage, however, is by upgrading your damage causing skills.

3) Generals like Oak can be as offensive as an Assassin. The minions are there to support him in battle, although he also has skills that can increase their power, like Morale or Surge of Faith.

1. Kill the minion, creeps more and caputring flags.  Don't focus on killing towers as it doesn't give you experience.   don't die.

2. Play Assassins, they usually do more damage.  Especially Unclean beast, he should give you enough damage to take down demigods from beginning to end game.

3. I suck with generals as well so I can't really comment.  I play generals just like I do wish assassins.  I don't buy any idols.

1.) Most often being lower level is caused by running to get flags too often and thus not killing minions and sticking in big group of demigods. The experience you get from flags while useful is less then you get from minions and all experience is split between the demigods in the area . Try to stay in a lane (Path grunts and easy to kill enemies take) as much as possible. Even if the lane has another demigod in it there is nothing wrong with running in killing minion and running out or waiting behind your sides tower wall and getting experience as the tower kills them. The favor items Heaven's Wraith is also useful as it allow you to get experience by killing minion on a completely different part of the map then where you are. Many player use this to level quickly and it's often more useful then the favor item that just boosts experience as it can be used to kill demigods which yield high experience quickly.

2.) Damage is less important then hitpoints and many new players make this mistake. Most player stack hitpoints as it works better then stacking damage items. Unbreakable boots, Nimoth's Chest Armour and Hauberk of Life are all items you should get early and often you should buy 2 or 3 of them depending on your build. That way you can last longer against other demigods and finish them off.  

3.) General can be played like Assasins many people don't take minion period the key is that any demigod should be killing creeps and other demigods as much as possible. Sedna is not a healer, the Queen of Thorns is not a shielder they should be in battle as much as possible and use their abilities to reinforce themselves and other demigods. If you use minion with very few exception you should also be attacking with them.

You can also send me a private message and I would be happy to have a 1v1 game where I could show you the basics.

the best way to level at a good pace is to farm creep waves in a lane. for most of the game you'll be competing against the other demigods for lane dominance. you'll gain experience if you're near an enemy creep when it dies. you'll gain gold in addition to that experience if you damaged the creep by at least 25% of its health. (you'll still get experience even if you didn't touch the thing at all). 

in order to maintain your lane staying power you'll need to have a good rate of health and mana regen. look for affordable early game items like Banded Armor and Scaled Helm to provide regen from the start of the game. 

you'll need to be able to harass enemy Demigods by damaging them. you might not get the kill, its usually possible for a Demigod to retreat before they get finished off in a 1on1 situation. but if you can get them to leave the lane they'll miss out on experience and you'll be able to farm the lane unmolested for a little while and accumulate more gold and experience. 

good harassing abilities are things like Venom Spit (on Unclean Beast), Fireball (on Torchbearer), attacking with your summoned minions while you stand back (any General can do this), etc. the key point is that you need to find ways of doing damage to your opponent without directly trading hits. 

There's a pinned post at the top of this forum that has all the answers you need.

Basically, pick the demigod you like (start with an assassin as they're a bit easier to manage) and pick a build for that dg.  Keep the build open in another screen or write it down on paper and follow it.   Do the same with items you want after reading up on ITEMZ (ie buy Banded Armor at the start go out and farm creeps as others have described until you have enough for the next item on your list).

If you follow the build for dg and items, you'll pretty much stay on par with the computer for most of the time (hard and nightmare difficulties get buffs that make them level faster).  Also, give up on being a dg killer until you've played a couple single player tournaments as going too hard for the kill is usually what get's beginners into trouble.  Just concentrate on getting 0 deaths for a game.

Generals are played pretty much the same way you play assassins, just that you have little guys running around you doing various things.  Once you get the hang of moving minions independently of your dg, the difference between assassin and general becomes pretty significant, but for now as a beginner general, just buy monks and then play as you would with an assassin.

Oh and just for clarity creeps = little guys who spawn at portals and run around the map on their own, minions = guys you spawn yourself and follow you around the map.

There really is a lot of reading involved with getting the hang of the game and that pinned article is the best place to start.