Venting emergency drain.

Code allows the use of a wet vent for the bathroom group which in my case is a sink, toilet, and shower drain. About 8-10 feet down stream of this group I have a washing machine drain with its own vent. I also need a emergency drain in my mechanical room. Does this need a separate vent?

yes, is the short answer. i am a upc plumber. the ipc drawing you have. altho code correct. if the vent is rolled, goes against everything i was taught
it is my understanding, that it was adopted, due to structursal restraints. and or difficult roughing in situations when the correct fall can not be achieved stacking the fittings.
so that said. can you add a vent or 2, that toilet will pump and the shower will gurgle. it wont happen today. but down the road
when the pipes no longer scour them selves and you get a little build up. on the walls of the pipe. the router rooter man will be your bestest friend. others will disagree or not

YOu show a "closed system". Which way does the water flow to the main line? You can connect the floor drain to the lavatory's vertical riser and comply with venting requirements. Your other drain, however, may not depending on the direction of flow.

I also need a emergency drain in my mechanical room. Does this need a separate vent?

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Only if you want it to remain sealed when any othe plumbing in the home is used.
Yes. By all means do all plumbing fixtures correctly. Some little used drains, like floor drains may even need trap primers to keep them from drying out.
A washer runing by that floor drain will suck it dry though.