How can I transition from carpeted stairs to an engineered hardwood floor?
One potential location is on the last rise on the stairs.  This is depicted below on my crude diagram.  Make the cut of the carpet right under the lip of the top of the 2nd floor.  Use a piece of trim to hide the cut and make it finished.



Other options include:


Create a small carpet landing at the top.
Take the carpet off all the stairs and make the stairs hardwood as
well.


Your second question:

Probably.  When you take the carpet up, see if there is a gap under the baseboard.  if so, see if the hardwood fits in the gap.  If so, you can leave it on.  If not, you should be able to carefully remove the baseboard, install the floor, and the re-attach the existing baseboard pieces when floor is finished.