I have an existing toilet and sink in the basement and want to install a tub. The layout is left to right: tub, toilet, sink. The sink has a drain that goes to the main. It also vents to a pipe that vents the laundry area. That vent runs along the wall about 4 ' up and runs behind the toilet and then comes out into the room about a couple feet and into the floor. When I jacked the floor, I can see that the vent tied into a t on the main drain (the connection was upright not on the side). I tore out the cast iron pipe to the toilet which also took that t with it. I replaced with 4" plastic pipe, put in a t and added the new toilet drain. I connected that t to the 2" drain that runs to the tub. On that 2" drain, I attached a t pipe about a foot away from the main to rerun the vent pipe over to the wall and up. That will reconnect to the vent pipe that runs along the wall, connects to the sink, and connects to the laundry. Question 1: Did I do that right? I've only dry connected it so far. I wonder if I should also put a t in further up the line on the 2" pipe and run that over to the wall too and connect into that long vent piece that goes to the sink and the laundry.
Question 2: should I build a platform to set the tub on so I have room for the trap? I don't like the idea of having an open uncemented section under the tub... what about bugs coming in? If not, how else would I do this so I can plumb the tub? The tub drain end would be against the same wall as the toilet and sink (not much room for plumbing unless I build it out). Thanks for your advice.

. Question 1: Did I do that right? I've only dry connected it so far. I wonder if I should also put a t in further up the line on the 2" pipe and run that over to the wall too and connect into that long vent piece that goes to the sink and the laundry.

The only tee that should be under the slab should be the tee venting the system and that tee should be upright or on a 45 degree angle. Use wyes or combination wye and eighth bends instead. You vent configuration sounds OK to me.

Question 2: should I build a platform to set the tub on so I have room for the trap? I don't like the idea of having an open uncemented section under the tub... what about bugs coming in?

Platforms are a hassle and don't look professional. We aways leave tub dapouts in the slab for a tub trap and raiser. If you're worried about bugs
Seal the bottom and sides with roof cement. Good luck, Tom

I'm a girl and this is my first big plumbing job. I can run copper pipe and solder it, but drain lines are my first. Can you explain what a wye and eighth bend are. I'll go to a plumbing store to get this stuff but like to kind of know what I'm talking about. I don't want to look stupid to those guys. Thanks.