You said you should end up in 5 Clubs. This is correct. The number of losing tricks in your hand is 5, which are 1 Spade, 3 Diamonds and 1 Club. You should open the bidding with 1 Club.
Your partner has 8 losing tricks (2 Spades, 3 Hearts and 3 Clubs) and since he can support your suit, he should bid 3 Clubs.
When you add your 5 losers, to your partner's 8 losers, you come up with 13, which when subtracted from 18 comes up with 5 - so you can now bid 5 Clubs.
Now go back to 52C and see how you do on the second question.