Documentation requirements

For a two-week trip you need only your passports. Visas aren't needed for US citizens to visit any of the countries you have listed unless you plan a long-term stay.

All the countries you mentioned, those of the Schengen zone and the UK allow US passport holders entry with passport only for personal travel within time limits. (much longer than your two weeks) There are no real limits as to how many times in that period you can enter and leave, as you mentioned, just present your passport.

For the UK, you will be given an entry form, you will need the address of your hotel and indicate your purpose in travelling there and how long you will be in the UK, but it is minor paperwork.

Yes.
Just make sure your passport is valid for 3 months past the end of your stay (so expires later than February 2017, since you are going for 2 weeks in November). If your passport expires in, say. December 2016 renew it soon so you will have a new one by your trip.

Both Schengen and the UK allow short visa free visits by US passport holders. So no visa to worry about.

It would seem that all we will need to do is present our passports at immigration, do I have that correct?

Going into any Schengen country, as many times as you want (without making them dizzy) during your short visit - yes.

Going into the UK, as many times as you want (without making them dizzy either) - yes, plus a Landing Card which will be given to you.

For the Schengen Area US citizens are allowed 90 days in 180 without a visa. You can enter, leave and re-enter the Schengen Area as many times as you like, so long as the total number of days does not exceed 90 in 180.
Your passport will be stamped every time you enter and leave the Schengen area, so there is a record of the number of days, but there are no checks travelling betwean Schengen countries.

If you are travelling between London and Paris on the Eurostar trains, both passport checks (UK and French/Schengen) are done before you get on the train.