Should I bid Two-Way Checkback and sign-off at 2 [diamond]? (this question could have been asked of a standard auction also….should I bid 2 [diamond] since I know partner has four diamonds)
No, you should pass 1 NT. You have a balanced hand with 10 HCPs. Yes, since your partner does not have four spades, you know he will have at least four diamonds. However, you are playing in a duplicate matchpoint game and the score for playing NT vs. a suit is much higher. Just pass 1 NT and go for the points!
How do you know partner has at least four diamonds? The only hand that will open 1 [diamond] with only three diamonds is a hand whose pattern is 4-4-3-2 (four spades, four hearts, three diamonds and two clubs). Therefore, when opener does not raise 1 [spade], he does not hold four spades and must hold at least four diamonds.