No. Current is volts divided by resistance. So 5V / 1.9 = 2.63A. I would choose a MOSFET that has a continuous current rating of 5A or more.
There will be a specified current specified at a Vgs voltage and the resultant Rds(on). The Vgs needs to be logic level (5V in this case) or lower and the current higher than the stall current.
No. Its continuous current is too low. You did not answer the question of do you want surface mount or through hole?