Can you connect sink waste vertically into horizontal pipe that exits rear of toilet at side of proposed new sink location.?

You can, I'm not sure that I would. Probably doesn't pass code for one thing. If that is not an issue, that is the main stack. Down to the sewer, up to the roof vent. If you attach a sink drain there, when the toilet is flushed, it will pull venting from wherever it can. Most will still come down from the roof, but being as close as it is, it will also pull from the sink drain and cause a gurgling from the sink. The other consideration is the sink itself. Make sure it has an overflow vent in the rim of the sink. If the one you use doesn't the drain will need a vent of its own, otherwise the sink drain will be trying to pull against a vacuum.

Another thought. They make what is called a Saddle Clamp to do what you are talking about. A half piece of pipe with a female connection in the side of it. Made of PVC and held on with two clamps that go around the existing pipe.