Unfortunately, the answer to these depend on the exact brand and line of contacts used. For example, here is a long list of silicon hydrogel lenses, and how long they last. Here is another list of materials used to make contact lenses (including many of the silicon hydrogel type). Some of those are dailies, but some can be worn day and night , such as the extended wear contacts listed here. You can usually look up your particular contact lenses online and find the maximum recommended time. However, I'd recommend (as would most eye doctors) that you generally wear them less than the maximum, just to be safe. For example, I use Biofinity lenses, which are approved to be worn for up to 7 days, but I usually wear them for no more than 2-3 days at a time.
The concerns here are how much oxygen gets to the eye, and how much material builds up on the contact lens. Some brands of contacts have much higher oxygen permeability, so you can wear them longer without damaging your eye.
Protein buildup is one factor in how uncomfortable contacts get, and it also depends on the material of the contact lens.
Similarly bacteria (and other microorganisms) buildup on your eye and contact lens depends on the material - and that will affect how long the contacts last and how long each day (or week) you can wear them.
No idea about the tears, but you shouldn't allow water to touch contacts. (Thanks Narusan for the comment).
Not aside from the same side effects that would be present for someone without contact lenses looking at a computer. Wearing contact lenses to fix vision is much closer to the natural optical system than glasses - so from and optical perspective, wearing contact lenses is almost exactly the same as having eyes that don't need correction at all. This is not true of glasses, which cause your muscles to move and your eyes to focus in different ways than they would if you didn't need glasses.