Minnesota uses the UPC; I did not check for amendments.
1) Your lavatory drain can wet vent the WC if you meet a few restrictions. First, the lav drain and vent have to be 2" (as shown); the lav trap arm can be 1-1/2" or 1-1/4". Second, the WC drain, measured along the pipe both vertically and horizontally from the closet flange to the wye where the lav drain comes in is limited to 6'.
2) The UPC requires 1/4" per foot slope for all drains. If you upsize the drain to 4" after all the fixtures, and you get permission from the AHJ on the basis that the pit would just be too deep otherwise, then you could use 1/8" per foot slope on the 4" portion.
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3) You show a vent line coming off the 3" line between the lav connection and the shower connection. That vent connection is not useful in that location, and your shower is unvented. With the connectivity order shown, the shower can not be wet vented, as the WC needs to be the last fixture on the wet vent. So you would need to move that extra dry vent to connect to the shower trap arm before the shower connects to the 3" line. And that horizontal jog you show in the vent would need to be at least 6" above the fixture flood rim (the shower curb in this case). Vent sections at 45 degrees from vertical are still considered vertical.
Also, just to double check, there can be no drainage coming down the dashed vent line from the story above. It needs to rise to the bathroom above and join a dry vent in that bathroom, one that is at least 2".
Lastly, I'm a little unclear on the cleanout requirements: whether it's OK not to have a cleanout for the portion of 3" drain between the WC and the wye where the lav drain joins; and whether the cleanout at the lav should be 3" (meaning the downstream drain would also be 3").
Cheers, Wayne