Can I tie my bathroom sink and utility sink drains together? As well as vent?

[vinceliberto]

In the picture you'll see my existing stack that was put in when the house was built for the basement rough-in. (Pay no attention to the hose coming out of the plug, it's a water softener drain that was not done correctly. I'll be taking care of that in another way.)

To the right of this picture i'll be installing a bathroom sink and to the right of that a utility sink.

My questions are:

1. - Can I bring the utility drain over to the bathroom drain and attach with a "T"?

2. - Can I use the existing "Y" in the stack for the drain or should I leave this as a clean out and put a new "Y" above the one in the picture?

3. - Can I again tie the two sinks together in the same manner for a vent and attach further up in the stack?