Can a turbojet jet or turbofan powered aircraft land and take off from water?
Yes, they can.

In service today: 

The Canadair CL415 is a turboprop water bomber with water landing capabilities (typically, water skimming capabilities, to skim across a lake and refill). 

The Shin Maywa US-2 is the latest in a series of rescue/maritime patrol aircraft that have been in service for some time. The design uses the engines and wing of a C-130, with an interesting STOL feature: ducts that blow air across the top of the flaps so that they can be set at a more extreme angle for extremely short takeoff. 

The Beriev BE-200 has seen limited production in Russia. It uses high bypass turbofans, mounted high and behind the wings to protect the engines from water spray. 

From the Soviet era, were the ekranoplan sea skimmers, that flew entirely in ground effects. All were turbine powered. 

In a prototype stage is the AVIC AG-600 in China. Powered by four turboprops, it appears to be an upsized copy of the Shin Maywa design.

A one-off production flying today is the Doriner DO-24ATT, essentially a WW2 DO-24 maritime patrol aircraft that was re-engined with turboprops. It is currently flown by Claudius Doriner's grandson. 

Four turbine powered amphibious/flying boat aircraft that were developed but never saw service were the Convair Sea Dart, Martin SeaMaster, Saunders-Roe Princess, and Saunders-Roe SRA1.