Expected value and Lotto ball problem involving Binomial and Poisson distributions

Question

So, my question follows on from this post: Probability of TattsLotto, problem and answer provided, need workout

I know how to calculate the probabilities from this post using the combination $\binom{45}{6}$ as the denominator (as per the post above) However, I have a couple of things I would like to work out:

1. What is the probability of winnings a prize? use the fact that $\frac{P(A)}{1-P(A)}$
2. If a ticket costs $1, how many tickets should be purchased to get an expected return of 1000 dollars?

I assume the first question invokes the Law of Total probability? And then the second question uses this fact to provide an expected value assuming that return is calculated directly from the odds.

Finally, how would I start to analyse the following:

3. If you have bought $1000 in tickets (one dollar tickets), what is the probability of winning a prize? (Use the Poisson approximation to the binomial dist. i.e. if n is large, and p is small, then a binomial dist. (n,p) can be approximated by a Poisson dist. with mean np).

Thanks for reading.

Edit: As pointed out, some of this doesn't make sense (That was my suspicion) here is the problem that was taken from some university lecture notes as an un-graded 'homework' problem: https://i.stack.imgur.com/VyXTb.jpg