You chose that your partner had 8 losing tricks. This is correct.
Here is his hand again.
There are 2 losers in Spades, 1 in Hearts, 3 in Diamonds and 2 in Clubs, making 8 in all.
You obviously have a hand worth bidding on. If we were using the normal system of bidding where you just go by points, with this hand you have 7 honour points and 1 point for the doubleton, since you have a suit fit in Spades with your partner. And according to that bidding system, you would bid 2 Spades - a supporting bid, showing 4 Spades and 6-9 points.
However, in the Losing Trick count system, your hand is worth more than this. Since you would be allowed to support your partner on 9 losing tricks, with a hand having only 8 losing tricks, your hand should be worth an extra trick. So you would jump bid and say 3 Spades.
Now let's go back an look again at the Opening bidder's hand.
Remember, you counted 7 losers to start with and opened 1 Spade. Your partner has now bid 3 Spades, so you know from his bid that he has 8 losers, rather than 9, and that he has at least 4 Spades.
In the other system of bidding, we would now revalue our point count on this hand, knowing we had a suit fit, and give an extra point for the doubleton. But with the losing trick count, we have already taken account of our shortage, because we only counted 2 losers in Hearts, so we cannot give our hand any extra values now. It had 7 losers before, and it still has 7 losers.
But to determine whether or not to go higher in your bid, you need to know the combined value of losers and what that means in terms of the end bid.
You add your losers (7) to your partner's losers (8) and you get 15. You subtract this number from 18, and you get 3. This tells you that you will make 3 on the hand, which is what you have already bid, and you should not go any higher. So you now No Bid, and all the others do too. You (South) are playing 3 Spades.
If you had originally had only 6 losers, you still would have opened the bidding with 1 Spade, but when you heard your partner's jump response, you would have added your 6 to his 8, and come up with 14, which when subtracted from 18 gives 4 - and you would have gone on and bid 4 Spades. But that was not the case in this instance.
Now we come to the opening lead by West.
Here is his hand:
52. What should West lead to the first trick?
a. Ace of Clubs
b. Ace of Diamonds
c. 2 of Hearts