Basement Bathroom Reno

I'm planning a renovation of an existing basement bathroom, it currently has a small sink on a vanity, and a toilet. I would like to add a bath tub to the bathroom, and will need to rework the existing drain and vent system.

The image below shows how I'd like to orient things, so I will be moving the sink and toilet away from the wall that separates the utility room and bathroom, to make room for the bathtub.

Each dark pink dot, shows where I would like to run a vertical vent for the sink, toilet, and bath tub. Then I will combine them and tie them into the existing vent, for the ejector pump (my sewer line is 1 foot from the slab grade).

Does this seem kosher? Or would there be a better way to route the vents and/or drain? The ejector pump pit is existing, and most likely has a 3" line running to it left-to-right in the image, straight to where the toilet shows up in the picture. I haven't jack hammered out the concrete yet.

Oh, and just to clarify, where the tub meets the main drain, I'd be using a wye with a 45* elbow on it, not a T.

Y

If your dimensions are anywhere near accurate, you will be using a "Y" heading towards the "P" trap with the vent combo where it passes under the wall.

More like this for the drain away from the sink, I don't know why I tried to draw that with it tying into the closet bend...

Does this look alright? I need to add a floor drain as well, there isn't one currently, I would like to put it where the yellow dot is...

Does the floor drain need a vent as well, I know it needs a trap?

Can I connect vents together with Ts on their sides? Or should I make it so that there is only wyes?