Building settlements over the sea
It's pretty obviously NO.

Page 2 of the rules  - 


  Except where noted below, Catan: Seafarers uses the same
  rules as The Settlers of Catan


On page 4 


  Shipping routes act as roads across water (or along the
  coast). You build and place ships in much the same way as
  roads


AND it specifically states


  If your shipping route reaches a coastline, you can then
  build a new settlement on that coast, even if it is a new island.
  Of course, you must still obey the “distance rule” from basic
  Settlers, even if you are building on a new island.


So ships are 'water' roads and you still need two hex sides between settlements/cities