Ok so for part A I did:

a(2)= -(2+1)cos(2^2/2)*2-sin(2^2/2)

a(2)= -4.083.

no
The speed of the particle is decreasing because the acceleration is negative. Correct?

half correct ... your calculation and reasoning is wrong.
And for part B I did:

V(t) -(t+1)sin(t^2/2)=0

V(0)= -(0+1)sin(0^2/2)=0

V(1)= -(1+1)sin(1^2/2)= -1.438

V(2) = -(2+2)sin(2^2/2)= -3.637

V(3)= -(3+2)sin(3^2/2) = 4.887

The particle changes direction when t=3 because the sign goes from negative to positive.

no ... the particle changes direction when