1.
V(23) * (1 + i) = q(38) * 5000 + p(38) * V(24)
2925 * 1.04 = q(38) * 5000 + (1 - q(38) ) * 3000
This simply means, reserve at time 23 with interest accumulated is equal to reserve at time 24 the benefit payout.
You should be able to solve for q(38)
2.
I may need to review a bit and answer this later. Sorry about that.