On hand 1 I agree with Quartz about opening 1NT (assuming you play 14-16 or 15-17) for exactly the reason he states - it solves your rebid problems. Yes, it is only 14 HCP but it is worth at least 15. If you open 1H, what do you bid over partner’s 1S? 1NT undervalues the hand.
Now it is tricky as to whether to show 5 spades. 6S scores more than 6C. I quite like 1NT - 2H; 2S - 6C. That should get the message across, and even if we are missing AS and AD, they’ve got to find the right lead.
Going more slowly
1NT - 2H
2S - 3C
3NT - 4C
4D - 5H (exclusion Blackwood)
6C (1 or 4)
The 4D bid might be a stretch. If partner bids 5C instead, I will give it a 6th.
If you do not open 1NT - some do not do so with a 5-card major; others require 3 in the other major - then what system are we playing? If 2/1, this gets into areas where even experts have differing opinions. After 1H - 2C, the next bid depends on what you play:
[ul]
[li]some play 2H as the default bid, i.e. when you have nothing else to show[/li][li]some play 2H guarantees 6 and bid 2NT even with no spade stop[/li][li]some require a spade stop for 2NT and 4-card support to raise partner, so bid 2H as the “least lie”[/li][li]some only raise on 3 with extra values, so bid 2H or 2NT[/li][li]others are happy to raise on 3, as suggested by K364[/li][/ul]
With the partner with whom I play the most sophisticated system, I play a bid of 2D here means “either diamonds, or nothing else to bid”.
So it is hard to give a sequence without knowing partnership agreements. If you play 3C as allowed on 3-card support, then K364’s sequence looks reasonable to me.
Hand 2.
This also gets us into partnership agreements playing 2/1. After 1D - 2C, does a reverse show extra values? I play that is does not, so the bidding would be:
1D - 2C
2H - 2NT
3NT - 4NT
It’s a poor slam. Manic leads aside, it needs JH onside and something else good to happen, e.g. hearts 3-3 or KS onside or play for the right squeeze.