Response to "convenient" minor bid
Assuming you are playing some simple form of standard american, yes your thinking was wrong on both hands.

Usually the responder is supposed to "bid up the line", giving preference to majors in case she has a 6-9 point hand.

With the first hand, you can either bid 1D or 1S. The reason to bid 1S instead of 1D is that the auction 1C-1D-1H-1S might have a special meaning (4th suit bids can have special meanings) and might show a stronger hand than what you have. Suit quality considerations are very rare when responding at the one level and your hand is not one of those rare hands.

With the second hand, you must bid 1H, and if partner bids 1S you can raise to 2S. 1NT actually denies a 4 card major.

The scoring in bridge gives preference to majors and as a result most bidding systems give preference to the majors. Bypassing 4 card majors when responding is usually considered bad.