Proper Venting for basement bath?

1. I would like to know if this is the proper setup for the DWV in a basement bath I have.

2. My second question is, are you allowed to vent out the sidewall of a house or do you always have to vent through the roof?

I hope this picture explains it well enough. The main picture is looking down from above.

EACH trap needs a vent. Now, all of those vent lines can be combined 6" above the flood plane of the highest item sharing the vent system. Inspectors often like 42" (nominal kitchen counter +6"), but it could be higher, depending on what's there.

The main vent stack must vent to the roof. Ventiing out the side of the building is not allowed.

vent

Depending on the actual demensions There could be several better ways of doing it, but one revision would be to not have the toilet vent horizontal out of the back of the tee. Most inspectors would not accept that tee, I assume you are showing a tee, on its back either.

Almost nothing would pass there, from the improper use of the sanitary tee, to the flat vent. This is why we get paid the big bucks.

So is the problem specifically with the toilet setup? Or is there also an issue with the vent for the Shower? I don't see anything wrong with the setup for the sink, is that correct?

If you are allowed to go horizontal with the vents, then this may work.
The wyes are rolled slightly up, and all fittings below grade are wyes, long 90's or 45's. The vented portion needs to be above the flow line of the waste line. This works in Seattle where the UPC plumbing code is in effect. What city are you buying the plumbing permit in?

Notice that the wye to branch off for the shower is before the vent for the toilet.

All of the vents need to go through the roof. Sometimes I've put them up the side of the house and penetrated through the roof with a flashing.