What protections and feedback does the fly-by-wire on the Boeing 777/787 provide?
1. Do they have the Alpha Floor or Flight Envelope protections Airbus aircraft have?
The Alpha Floor protection on an Airbus overwrites the thrust setting commanded with the thrust levers to TOGA. Boeing does not do this. The autothrottles (if armed) will engage to prevent a stall, but the computer never overwrites the actual thrust lever position in the cockpit:

With the autothrottle armed, the autothrottle automatically activates if not autopilot
or F/D is active or and autopilot or F/D is in VNAV XXX, ALT, V/S, or
G/S, and:

speed less than FMC calculated value for one second
thrust below reference thrust
airplane altitude above 100 feet RA on approach, or airplane barometric    altitude 400 feet above airport on takeoff

Note: During a descent in VNAV SPD, the autothrottle may activate in HOLD mode and will not support stall protection.

(Boeing 777 FCOMv2 4.20.9 - Automatic Flight - System Description)
Also, unlike an Airbus, this protection can be disabled by simply disarming the autothrottle using the switch on the MCP.
The Boeing 777 and 787 do however have Flight Envelope Protections. These also work a bit differently than in a modern Airbus, where sidestick inputs are simply ignored or limited by the computers. In a Boeing, the flight envelope protection will use artificial forces on the yokes to provide the following:

Flight Envelope Protection
The flight envelope protection system reduces the possibility of
inadvertently exceeding the airplane's flight envelope. The flight
envelope protection system provides crew awareness of envelope margins
through tactile, aural, and visual cues. The protection functions do
not reduce pilot control authority. The protection functions are
described later in this section and include:

stall protection
overspeed protection
roll envelope bank angle protection.


(Boeing 777 FCOMv2 9.20.5 - Flight Controls - System Description)
It says that the pilot control authority is not reduced because the pilots can always overpower the simulated forces on the yoke and command the aircraft to go beyond the protected flight envelope.
Essentially, the philosophy for the control authority differs:

Airbus will not let you do control inputs that might get you killed.
Boeing will stop you from accidentally making control inputs that might get you killed, but you can overwrite them.

See also:

What are the main differences piloting Boeing vs. Airbus aircraft?
How does envelope protection work in Airbus vs. Boeing aircraft?

2. Do they have force feedback/force feel?
Yes, unlike an Airbus sidestick the Boeing 777 and 787 simulate the forces on the yoke and therefore provide force feedback:

The primary flight control system uses conventional control wheel, column, and
pedal inputs from the pilot to electronically command the flight control surfaces.
The system provides conventional control feel and pitch responses to speed and
trim changes.

(Boeing 777 FCOMv2 9.20.1 - Flight Controls - System Description)
You won't see the yoke shake in turbulence like on a 737, but you will see or feel the autopilot inputs as the yoke moves.
See also: How does the Boeing 777&#39;s yoke of both the captain and the first officer have synchronized movement?
3. When banking (without any pitch input), will the aircraft start to descend, or does the system counteract it like in an Airbus?
It will counteract like an Airbus, up to 30° bank angle, so you can fly a turn by rotating the control wheel only:

The PFCs also provide compensation for flap and speedbrake configuration
changes, and turns up to 30° of bank. The PFCs automatically control pitch to
maintain a relatively constant flight path. This eliminates the need for the pilot to
make control column inputs to compensate for these factor. For turns up to 30°
of bank, the pilot does not need to add additional column back pressure to
maintain altitude. For turns of more than 30° of bank, the pilot does need to add
column back pressure.

(Boeing 777 FCOMv2 9.20.10 - Flight Controls - System Description)
The PFCs here are the three Primary Flight Computers.