Diablo – How does Shield Bash (Shattered Shield) work

Yes, dodge simply gives to attackers a x% to miss their attacks. It works on all attack types:

• Melee Attacks
• Ranged Attacks
• Ranged Spells
• Ground-based AoE

Dodge does not work only against status effect modifier like fear, jail, etc.

Dodge is linked to dexterity and seems not hard-capped but its formula has a diminishing effects like explained in this answer.

2000 Dexterity, for example, provide you a 40% dodge:

100*0.100 + 400*0.025 + 500*0.020 + 1000*0.010 = 40%

You are correct that a snare slows the targets down for a set amount of time.

While looking at the tool tip of a skill that has a snare effect press the control key. This will give you detailed information on the skill including but the duration of the snare and the reduction of movement speed that will be applied to the target.

While it is possible that your skill with snare on it will have other effects, it is not usually a direct result of the snare component of the skill itself.

Lastly, no, not all snare effects are equal and pretty much all of them are altered in some manner through runes. You can use the tool tips with the control key mentioned above or even just browse snare causing skills from the link @heishe posted in the comment to the question (Like here is a snare skill with extended duration for a demon hunter: http://us.battle.net/d3/en/calculator/demon-hunter#b!!b)