The guy at Home Depot just proved to you why he is stocking shelves instead of working in the plumbing trade. Using an 1-1/2" trap as suggest by the Home Depot clerk would be two code violations. 1. A shower is required to have a 2" trap and a 2" drain line & 2. The drain basket in the base of the shower already has a 2" discharge and code strictly prohibits reducing the size of a drain line in the direction of flow. You may need to consult a framer about sistering that joist so you can notch it. The plumbing code prohibits any notches on the top of a floor joist in the center 1/3 of the overall span. On the outer 1/3 of the joist you may notch to a depth not to exceed 1/6 the height of the joist. (a 2x10 could be notched a maximum of 1-1/2").

Kike99gt asked a legitimate question which seems to have been overlooked here. Is PVC preferred over ABS? The answer is no. PVC and ABS should be thought of as about equal in performance and expected life. PVC is probably the material that is most widely used but some local jurisdictions limit DWV piping to ABS only. Why you ask? ABS (Acylonitrile Butadiene styrene) pipe is only manufactured for DWV applications under the IPS (iron pipe standard) wall thickness sched. 40 in sizes ranging from 1-1/4" through 6" under ASTM(American Society of Testing & Materials) standard ASTM D-2661. By contrast, PVC pipe is manufactured for Electrical conduit, pressure piping, DWV piping and well casing and the wall thickness standards range IPS Sched, 20, 30, 40, 80, 120 and 200. In addition, PVC is also manufactured under the SDR Standard Dimension Ratio) wall thickness standard. Under the SDR standard the wall thickness can be mathematically determined by dividing the diameter by the index number. I.E. A 2" SDR-30 pipe would have a wall thickness equal to 2" / 30 = 0.066" PVC pipe intended to be sued as "pressure pipe" will be labeled as approved under ASTM D-1785 PVC pipe approved for use as DWV pipe will be labeled as approved under ASTM D-2665 PVC pipe approved for well casing will be labeled as approved under ASTM F-480 The plumbing codes state that all DWV piping inside a structure MUST BE sched.40 pipe. While they do make some PVC sched.40 pipe that is labeled solely for DWV application as a rule all other PVC sched 40 pipe is labeled as approved under ASTM D-1785 & ASTM D-2665. This explains why when installing PVC pipe we are required to install it in such a manner that the writing on the pipe wall is clearly visible for inspection and most inspectors will red tag any section of PVC where they cannot see the writing. In some jurisdictions, rather that rely on the inspectors to see all the pipe they simply demand that we use ABS pipe, which is only manufactured to DWV specs.

'Now, the tub and sink are not vented correctly or (it seems like) at all.' Was the plumbing job inspected? Was it performed by a licensed plumber? Both are required for a commercial building, not just for the current rental units. Have you opened the drum trap to make sure it is clear of debris? What's the slope on the tub drain line from the drum trap to the wall? Your pics show no slope and no vent. Are S-traps legal in your area? Not in mine. P.S. The wiring job looks questionable, too.

Pressure fittings are defined by the angle of the change in direction they make. I.E. a 90 deg elbow, 45deg elbow, 60deeg elbow etc. In order to help insure we don't mix them, DWV(drain,wste & vent) fittings are defined by the fraction of a circle the change in direction makes. A full circle is 360 degree so a DWV 90 deg elbow would be 360/90 = 4 or properly its called a 1/4 bend. 60deg = 1/6 bend - 45deg = 1/8 bend. A common fitting has a female hub on each end but a "Street fitting" has a female hub on one end and a male raw pipe size on the other end. To make the offset you would begin with a Street 1/8bend with the male pipe end directly into the TEE of the waste & overflow. This would change the direction to 45 degress. Install a length of PVC in the female hub of the 1/8 bend and run the offset down at 45deg to the point where your trap will be. On the bottom end of the 45 deg offset pipe you install another street 1/8 bend with the pipe into the female hub, This will change the direction from 45deg slant to vertically down and it would leave a raw male pipe end that will fit directly into the input of the P-trap. You will find the fittings in both ABS and PVC at any local hardware or home supply store. The choice of which material to use is determined by what kind of pipe you have now. Code prohibits glueing dissimilar plastic so if you have ABS you would use ABS, if you have PVC you would use PVC. In this case you have cast iron so you may use either material as long as all the pieces are the same material.