They should be 10, and 0.1811 respectivly.
The first involves no calculation at all, just knowlege. A Poisson process with a mean of n occurences in a time t, has a exponential distribution of inter-occurence times with mean being t/n, so in this case we have 0.1 per week, so the mean time between taking on new employees is 0.1/1 weeks.
For the second use the Poisson to calculate the probability p that exactly two employees are taken on in a week. Then use the binomial distribution B(50,p) to calculate the probability that exactly one week sees two new employees b(1;50,p).