There’s a variety of ways for this problem to occur, so let’s start with the basics. Is the battery in good condition? Even though it may show 12 volts on a tester, when you actually apply a load to it (via the starter motor) you may find it loses the plot. And modern, fuel-injected engines hate having low voltage when they’re trying to start or run.

The next thing to check would be whether you have power at the coil packs. If you don’t, you need to work your way upstream to find out where the power stops. The fuses and relays for the ignition are a likely culprit. And don’t forget to make sure the coil packs are earthed properly. Bad earths are an incredibly common way for modern engines to go haywire.

Moving out of a Statesman you will probably want some luxury, so that's definitely not a Captiva. I'd suggest you test drive a CX-5 and a Subaru Forester, both of which get The Tick, and choose between them.

It's not unusual to have explosions like you experienced, in fact   it's relatively common. The explosion occurs when the air/gas mixture in the intake manifold ignites and the rapid expansion of the gas mixture often blows out the air cleaner like it did on your car.   Ignition is usually caused by a random spark, so you have to find and fix the cause of that spark. The mechanic was on the mark when he suggested you change the spark plugs and clean the throttle body, and I would have changed the spark plug leads as well. His advice that it would settle down is wrong, it will continue to occur until the cause is identified and fixed. He's probably hoping that you will have left town by the time you realize his advice in this case is incorrect.