Bathroom drainage and venting

[tatertot]

I hired a handyman to convert a 1/2 bath to bull bathroom in my basement and am fairly sure I found a few code violations. I am looking for some help confirming before I talk to him tomorrow morning. I am considering contracting with a plumber to get this fixed correctly and letting the handyman finish the rest of it. What flagged the issue is that they did not leave enough room for the toilet. I started reading the IPC and am fairly sure I found two additional code violations.

1) Toilet is not vented properly, the vent needs to be downstream of the toile drain, I think this can be fixed by either relocating the vanity drain and vent (concrete will be to be reopened) or adding a dedicated vent for the toilet
2) Use of a sanitary T at the toilet connection

Is there anything I missed? Thoughts the plan to fix this? I attached a couple pictures.

 

[breplum]

You definitely and totally wasted your money on that handy man.
Number ONE issue: Tees may not be used in the horizontal plane. Not for a WC, ever, nor on side layout.
You need a plumber, but will probably need to demo more because even with horizontal wet venting, the drains cannot go into the WC like that.