I'll try to answer what I can even through I don't really have a high level monk yet. most of these questions are pretty much genereal "how does the system work" ones anyway. (actually think it would have been fine staying in general discussion)
I've started using a Monk recently, and I've found that I enjoy wielding two weapons. However, I'm a bit confused on how it works. With that being said, I have a few questions.
1. Does both weapon's damage combine into one for a single attack? Meaning, if I have two weapons with 10 damage, is my DPS now 20?
You alternate weapons every time you attack. So for example, let's assume a weapon that does 10 damage in the main hand, a weapon that does 20 damage on the off hand. For this example we'll assume you use a skill that does 100% WD with no cooldown. Every time you use that skill you alternate so your first attack with that skill will do 10 damage, the second will do 20. This continues ad infinitum.
2. How is attack speed calculated when both weapons have different attack speeds? Is it averaged out or does it use the highest or the lowest of the two?
Attack speed on your character sheet only shows the attack speed for the current weapon that's about to strike. You are given a 15% attack speed bonus on both weapons for dual wielding. For example, if you have a mainhand with a 2.0 attack speed and an offhand with a 1.0 attack speed and you haven't attacked yet, your sheet would show 2.3 attacks per second. After you attack once, the character sheet will swap over to the offhand weapon speed and then show a 1.15 attacks per second.
You can see this happen in practice as your first attack animation will be much faster than the second one.
3. Lastly, is it better to just use a shield off-hand?
This depends on what you want to do. If you need survivability then using a shield is great. It gives you lots of extra armor and the stats that might be on the shield. If you're having a hard time surviving this might be a good idea to try, otherwise a lot of monks, or melee characters in general, tend to prefer using two weapons and supplimenting it with another survivability stat like Life on Hit. With lots of life on hit, you don't really need the extra armor.
This question has no right answer. It's going to based on your gear and what gear you find or buy. It's also going to depend on what your playstyle is. I know 90% of monks don't use 2h weapons, but that option is also availlble to you, especially after the wave of light buff that just came through.