1.) What dia. Drain pipe is used for the shower/tub? 2" ? Is that ID or OD?

2.) What dia vent pipe is for the shower/tub? 2"?

3.) I'm going to put a vent in for the shower/tub in my basement. It starts at the slab then goes straight up about 7ft. And then does a 90 and then is running between the floor joists for about 6ft. Then there will be another 90 to have the vent go down the ext wall about 5" and then another 90 for it to run horizontal just under the joists for about 3ft and then another 90 where it goes down and then it taps into the toilet vent. Hope that isn't confusing. I have to do something like this becuase I can run it through the walls as they are 2x4's.

3a.) My question is... I read that there has to be a slight grade to the vent pipe to prevent condensation build up, is this true?

3b.) As I outlined above, can I do all these routings? Also, is there a max distance you can route away from the vent stack? or vent from the shower/tub?

4.) What is the diameter of the sewer drain/line below the basement floor running out to the street? 3"?

5.) If I'm going to connect my shower/tub drain (PVC) to the sewer line (Cast Iron), what type of fitting do I need. I know its going to be a 45 degree 7 plus one opening will have to be the size of the tub drain dia and the other two openings will be the sewer dia. How do you connect PVC to the Cast Iron?

6.) When connecting the shower/tub drain to the sewer drain, can the slope be greater than 1/4" every ft?

7.) Which is easier to install from a plumbing perspective, two handled faucet or single handled faucet for the shower?

7a.) Which one do you prefer and why?

8.) How many fixtures can be tapped into the main vent? I have two now and what to put a third.

9.) Which water supply valves do recommend so they seal the best and don't freeze up over time?

9a.) Gate valve, fixture shutoff valve, vacuum breaker?

10.) How many T's can you have off one water pipe line? I have two splits off it currently (one goes to the basement toilet and the other goes to the upstairs shower). I want to add a third? Would I lose water pressure?

1.) What dia. Drain pipe is used for the shower/tub? 2" ? Is that ID or OD?
2" ID.
2.) What dia vent pipe is for the shower/tub? 2"?
If that's all it's venting then 1 1/2" ID will do.
3.) I'm going to put a vent in for the shower/tub in my basement. It starts at the slab then goes straight up about 7ft. And then does a 90 and then is running between the floor joists for about 6ft. Then there will be another 90 to have the vent go down the ext wall about 5" and then another 90 for it to run horizontal just under the joists for about 3ft and then another 90 where it goes down and then it taps into the toilet vent. Hope that isn't confusing. I have to do something like this becuase I can run it through the walls as they are 2x4's.
As long as it's a vent the twists and turns don't matter.
3a.) My question is... I read that there has to be a slight grade to the vent pipe to prevent condensation build up, is this true?
You will slope back to the drain from the vent connection using 1/4" fall to the foot. Also you must invert the fitting you're connecting to the main vent stack.
3b.) As I outlined above, can I do all these routings? Also, is there a max distance you can route away from the vent stack? Or vent from the shower/tub?
Your vents fall within code. There is no limit to a vents length.
4.) What is the diameter of the sewer drain/line below the basement floor running out to the street? 3"?
Under the cement floor the sewer main's 4".
5.) If I'm going to connect my shower/tub drain (PVC) to the sewer line (Cast Iron), what type of fitting do I need. I know its going to be a 45 degree 7 plus one opening will have to be the size of the tub drain dia and the other two openings will be the sewer dia. How do you connect PVC to the Cast Iron?
You don't connect your shower/tub to the sewer unless it's got its own vent.
You connet it to the lavatory dtain where it will be wet vented. How you convert to PVC from cast iron will depend on the cast iron fitting you're converting from.
6.) When connecting the shower/tub drain to the sewer drain, can the slope be greater than 1/4" every ft?
As explained above, you don't connect to the sewer without venting the tub.
keep your slope a 1/4" to the foot and then 45 down to make the tie in. Too much fall will allow solids to drop and build up.
7.) Which is easier to install from a plumbing perspective, two handled faucet or single handled faucet for the shower?
Both hook up pretty much the same way.
7a.) Which one do you prefer and why?
I prefer the single handle cartridge type such as Moen. The reason being the ease of repair.
8.) How many fixtures can be tapped into the main vent? I have two now and what to put a third.
This is determined by the size of the main vent and the number of fixture units assigned to each fixture. Since you failed to supply me with the details I can't answer your question.
9.) Which water supply valves do recommend so they seal the best and don't freeze up over time?
We use BrassCraft 1/2 X1/4 cheome angle stops. To prevent freezing up over time open them all the way up and then back off 1/4 turn.
9a.) Gate valve, fixture shutoff valve, vacuum breaker?
Is there a question here?
10.) How many T's can you have off one water pipe line? I have two splits off it currently (one goes to the basement toilet and the other goes to the upstairs shower). I want to add a third? Would I lose water pressure?
Code will allow 3 fixtures off a 1/2" branch supplied by a 3/4" main. Any more then that will lose you both pressure and volume.
Good luck, Tom

I've attached a drawing to show how the shower/tub drain will be connected to the sewer line. The toilet drain and main stack drain are existing and drawn according to how they are positioned as of today. The drain line and vent line for the shower/tub is how I want to connect everything.

1.) Can I connect the shower/tub drain lines to the sewer line this way?

2.) Can I connect the vent pipe for the shower/tub as I have it shown connecting to the toilet vent (about 4ft up on the wall) on the back wall or do I have to run it past the toilet vent and to the main vertical vent in the right corner?

Oops, forgot to attach the drawing.

1.) Can I connect the shower/tub drain lines to the sewer line this way?
Yes.
2.) Can I connect the vent pipe for the shower/tub as I have it shown connecting to the toilet vent (about 4ft up on the wall) on the back wall or do I have to run it past the toilet vent and to the main vertical vent in the right corner?
You may revent the shower vent back into the toilet vent and combine the two.
Good luck, Tom