Why a Common Trip electrical panel?

Hi,
I need an expert opinion. They replaced our independent breakers with Common-Trip ones on existing wiring. Is this right?
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Images here:
Tripped breaker: https://newport.smugmug.com/Solar-and-roof-install/i-XJzQq8k/A
Full panel: https://newport.smugmug.com/Solar-and-roof-install/i-mhPhjdQ/A
Wiring: https://newport.smugmug.com/Solar-and-roof-install/i-dfh9TDK/A
Old panel (after removal): https://newport.smugmug.com/Solar-and-roof-install/i-QRRgfjz/A
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Background: We got solar a month ago and had to replace our 1972 era 100A panel one with a 200A. The solar company sent their electrician who does this daily.
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Yesterday our over-the-range microwave dedicated circuit tripped yesterday, and the dishwasher's dedicated circuit tripped with it. The microwave seems fried; it blows the circuit within 2 seconds of trying to run it. When plugged into another outlet, it blows that circuit too, along with the circuit it's paired to.
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I did a little research. Apparently these days, using 12/3 in a 240V split (split to two 120V) with "shared neutral" is a thing for saving wiring, but our house was already wired 52 years ago. It's all 12G and all circuits are grounded. The previous panel was all independent circuits. This was 3 weeks ago and now, coincidentally, our over-the-range now needs replacement.
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I also notice that many of the trip switches are physically paired, but some aren't.
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1. Is it safe, or could it be sending extra electricity to some circuits?
1a. Could it be sending a surge to the paired circuit when it blows (over what would be normal to all circuits)?
2. Is the only downside that we trip more outlets and appliances when something blows?
3. Are there advantages to this method, when paired with existing (independent) house wiring?
4. Was this necessary, or did they saddle us with an inappropriate panel type?
5. Why are some ganged together, and some aren't? Even those not ganged seem to trip in pairs.
6. Looking at my old circuit, I notice the OVEN and AC each had dual 30A breakers. The new ones are single 30A breakers. Does this look right? 30A seems a little low, but 60A would be high (wouldn't it?). It's Winter so we won't be running the (3 ton) AC until next year. The oven is a typical 30" Kenmore Elite built-in residential electric oven, mounted under a gas stovetop. We've run the oven a few times without tripping breakers. Hmm.

Thank you!