A:
Yes, you have to cut off the nose or overhang on the existing tread to that it's outside edge is even with the riser below. You will need to install a stair nosing on the outside edge of each tread. But first:
After you have cut all the over hangs off, start with the bottom riser.
Install from the floor to the top edge of the first tread. Install the first nosing on the first or bottom tread. You can use Bostik's Best urethane adhesive for best grab. After the first nosing is installed, start off the edge of the nosing and install the flooring up to the next riser.
Install the second riser as with the first and install the nosing for the second step. Continue until you reach the top riser. You can use a pneumatic trim gun if you like to hold the pieces in place. Shoot onto the top of the tongue as far as you can and the last board near the riser can be nailed close to the riser so that when you install the wood on the riser the nail will be hidden. I now digress. The nosing may have a groove on it. If it does, you can use a spline in the groove which will also slide into the groove on the first board. If not, you may need to fire a couple of nails into the top, near the edge to hold that one row down. That is about it.

