Not sure how many people share that "common definition". Most people I speak with day-to-day (who understands blockchain in the first place), would consider "programs stored on blockchain to run when conditions are met" as the most defining feature, and doesn't have to be turing complete for doing so.
Yes. I would have designed contracts as decision tables.[1] Those are not Turing-complete. They look more like spreadsheets. They have a finite number of cases and can be exhaustively tested.
Absolutely, Bitcoin smart contracts are different than Ethereum smart contracts. What's your point? Doesn't mean one has smart contracts and the other one doesn't.
Are you seriously going to grandstand whether the word "smart contract" can include non-turing-complete runtimes?
No, Bitcoin does not have smart contracts. It has a limited scripting environment that you can't do much with other than colored coins, and we've all seen how that's played out.