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So I have a new shiny board that has trench works covering both sides. As I look at my three leman russes I wonder how would a tank handle a trench line like this. The Tanks themselves only fit into a couple of parts of the trench and I have many a question resulting from this.

1 Can a tank cross a line of trench work? It isn't wider then the tank but it is long enough that the tank would fall into the trench before inertia would carry it to the other side. It dips in a thirty degrees (about) when inside so I would think this would destroy them. On the other side tanks are designed to be robust and were origionally designed to go right over a trench work sweeping it with machine gun fire before moving along to the next.

2 If a tank is inside a trench to start can it get out? Would they have built ramps for them to move out of when necessary or would it be like a fighting hole that you could move back and forth in.

3 Can a tank move into a trench? In the areas where a tank could fit in could it run on in without damage or would this just be to much for even an armored behemoth to take.

4 Assuming a tank can run over a trench would the occupants of that trench suffer tank shock? I would think it would be fairly traumatising. If a tank can't and rolles into the trench at a thirty degree angle never to move again does that count as tank shocking.

5 If their were say sandbags along the parapet that a tank runs into do I just ignor them? Do they fall into the trench and cause damage? does the tank run aground on them?

There are probably more questions to be had but I have stuff to do so thats all for now.

Most of those specifics are abstracted by rule difficult/dangerous terrain rules.
You would have to declare which parts are impassable/difficult/dangerous before the game.

4 Assuming a tank can run over a trench would the occupants of that trench suffer tank shock?
    Technically, yes since the tank is occupying the same space.
    Unless the tank is clearing not interacting with the troops below.
    ie if the tank is on a completely separate level above.
    Which is this scenario I wouldn't image that to be the case, since then the models in the trench would be surrounded by wall that they could not fire over

Terrain is non-deformable (with the exception of creating craters) in basic 40k.
To add the level of trench warfare detail you seem to want, I'd suggest you write up the specifics yourself.

Agreed with Belphegor. All of this is abstracted within the rules already; Decide before the game how the terrain affects models, and what types of models, if any, are affected differently. It's perfectly acceptable in friendly games (including {or maybe especially} Campaign games) to use special rules for your special terrain. In tournaments, the TO will inform players of any terrain rules that aren't covered in the book, or of any terrain pieces whose rules are not mutable, I.E. decided by the players before every game.

If it comes to writing special house rules for this situation, I'd say narrower trenches would be difficult terrain at worst for tanks.

40k tanks are heavily influenced by WWI tanks, right down to the inclusion of sponson weaponry. Part of the purpose of a tank in trench warfare is to drive right over an enemy trench and "bridge" it, and then use the sponson guns to pour enfilade fire down the line of the trench in both directions.

Tthis is the perfect situation to use this rule:
clear it with the opponent before the stat or the game. In a turrny get the/an official to settle it before the start.

You should have a look at the Seige of Vraks books - lots of info on using trenches in games.

1. A tank should be able to cross a trench that is less than half the length of the ground contacting length of the tracks wide. If it's wider then that then it'll nose in and get stuck. Try it with the model - if you keep nudging it forwards does it hit the other side in a position where it could pull itself out or does it dive into the trench?

2. It would need ramps to get out unless the trench is very shallow. Is the lip of the trench low enough that the angled part of the treads get onto the top of it? If so then it's got a chance. Russ's and Raiders might be okay - rhinos have got no chance.

3. If there's room to move then it should be fine.

4. Although the tank isn't going to be able to hurt anyone it is going to scare them. A tank shock represents this quite well. It also gives you a chance to go after the exposed underbelly (I'd allow shots against rear armour)

5. Are the sandbags removable? If so then you could come up with rules for knocking them down. Otherwise I'd suggest treating them as completely solid purely for the sake of game flow.

Since it sounds like some of your trenches are quite big you may want to equip some of your tanks with trench rails to help them accross or make a bridging vehicle for the really big ones.