"MikeMac" writes:
1: the tailstock head spins slowly with the piece, but not at the
same speed.. is that normal?

No. Tighten it just until they turn at the same speed.

Note: Don't use tailstock pressure to embed the drive center into the
wood. Examples of how to do it right:

1. Remove the drive center and hammer it into the wood with a mallet,
then replace it in the lathe.

2. Use a bandsaw to cut an X or + in the end of the wood, perhaps
pre-drilling a small center hole, so that the center catches without
pressure.

3. pre-drill a hole narrow enough that the center's wings *almost*
touch the wood. Install the wood with the tail center lightly
touching. Hold the wood and turn on the lathe; the drive center
spins and the wood just sits there. Gradually tighten the tail
center until the drive center starts cutting (yes, cutting) the end
of the wood. This gives you a perfectly flat surface, which
requires less pressure to grab. Now, let go of the wood and
tighten the tail center a little more.

In all cases, pre-drilling a small hole is useful for smaller blanks,
where the splitting action of the center might split the blank. Or,
get a center with a spring-loaded point.

2: the piece oscillates ever so little.. If I back off the
tailstock head a bit, the tailstock pin stops turning, & the
oscillating stops. Is that normal?

No. If you press *too* hard with the tailstock, you could bow the
wood, which is bad.

3: If I line up the point of the headstock, and the point on the
tailstock, the don't line up perfectly.. (less than 1 mm diff).
Does this really matter?

Yes. They should be so close you can't see any deviation.