Basement Bathroom Rough In

I'm getting ready to add a basement bathroom to my 50 year old bungalow. The cast iron main drain is located fairly close to where I plan to install the bathroom and is located about 18 inches below the slab. I have two questions and have attached two crude drawings (not to scale) to hopefully show what I'm wanting to do.

As mentioned, the main drain is about 18 inches below the slab. Can I install a "Y" in the vertical position and run a 3" drain pipe above the existing drain pipe? This would make it much easier to tie in the new drains for the sink and bathtub, plus the existing drain is not located exactly where needed. This is my second diagram.

The first diagram is my proposed layout. The diagram is rather crude, but hopefully I've explained things well enough to get opinions on whether or not the layout is acceptable.

Thanks in advance.

No part of the vent can run horizontal until it has risen vertically to a point 6" above the flood level rim of the hghest fixture served unless it is a portion of a wet vent and then it has to be properly sized and washed by a fixture above.

Is my horizontal portion of the vent not considered a wet vent, thus being allowed? It will be washed by the sink that is tee'd into it on the vertical.

As drawn, the toilet is wet vented through the lav but the tub trap will still be siphoned by the toilet flushing.

try a double y fitting to attach the tub and sink at the same point. Check with local codes if that is acceptable. sink drain needs to be 2". instead of verticle roll the 4x3 y off on a 45-50 anlge and correct back to 1/4" per ft grade wit the 45. this will keep your new 3" just above the 4" but still deep enough to help you maintain grade on your new pipe.