With 13 HCP you should open the bidding. If you have 5 cards in a major suit you want to open 1 of that major. If you do not have a 5 card major but do have 13 HCP you still need to open the bidding. Since you don't have a 5 card major open the bidding 1 of your longest minor. This might only have 3 cards in it.
Therefore to open the bidding 1♦ you need 13 HCP and 3♦. That's it.
When partner opens 1♦ we no longer need 13 points to make a bid. Since partner opened the bidding they have the opening hand. We just need 6 HCP to respond. With 6 HCP we need to respond. To bid a new suit we just need 4 cards in that suit. To support partner's ♦ suit we should have 5 cards in the suit. (Partner only need 3 cards in the suit to open remember. So to get an 8 card fit we should have 5.)
If partner opens 1♦ and you have a fit but you also have a 4 card major, bit the major suit. You want to try to find a fit there. If you do not have a fit in the major you can always bid ♦ later on.
The only bids that limit your hand are 1NT and 2♦. Both these bids limit your hand to 6 to 10 points and partner can pass both those bids.
If you respond with a new suit at the 1 level you might only have 6 points, but you could have 13 points -- or even 20 points. Partner MUST bid again with any of these bids. But we can let partner worry about that.
If you respond with a new suit at the 2 level you must have at least 10 HCP. Therefore sometimes you might have a hand with ♣ that you can't tell partner about. You might get stuck bidding 1NT with an unbalanced hand or you might have to bid a shorter major suit rather than a longer ♣ suit. Such is life.
Therefore if your partner opens the bidding 1♦ here is a table that that states your only possible responses if you have 6 to 9 points:
Bid
Points
Number in suit
1♥
6 or more points and
at least 4 in the suit
1♠
6 or more points and
at least 4 in the suit
1NT
6 to 10 points and
no 4 card major suit or 5 card ♦ suit
2♦
6 to 10 points and
at least 5 cards in the ♦ suit with no 4 card major suit
With two 5 card suits bid the higher ranking one first. With two 4 card majors bid them up the line so ♥ first.
With that in mind what do you respond when your partner opens 1♦?
Hand 1
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