You say the battery is okay, and it’s possible for it to show 12 volts on a multi-meter, yet still be ready to be replaced. The trick is to load test the battery. That is, measure the voltage across the terminals while the battery is trying to crank the engine. Sometimes, a battery that seems okay with no load will turn to jelly once you apply the starter-motor load.

Cars (and batteries) don’t like sitting around doing nothing. The car’s alarm and even things like the clock in the dashboard will all continue to run, slowly draining the battery. A drained battery, if sat long enough, will often not recover even if you try to recharge it. Beyond that, an auto electrician will be your best first stop.

Without knowing more, your problem could be caused by quite a few different things, including wheel bearings, driveshafts, brake rotors and even worn suspension components. But a really common cause of a vibration at a particular speed is a wheel that has shed one or more of its little balancing weights.

Given the parlous state of this nation’s roads at the moment, hitting a big pothole is a pretty good bet right now. And the shock of that impact is a typical way for the wheel to shed its balance weights. These small, lead weights are added to the wheel when a tyre shop fits new tyres. The idea is to use the lead to balance the wheel so it spins smoothly. Lose the weight and you suddenly have an out-of-balance wheel and tyre and a vibration is a likely consequence. A good tyre shop will be able to check this for you.

That's quite high mileage, but in a modern car with vastly better metallurgy, engineering design and oil quality (particularly multi-grade oil) it's not impossible for a car with that sort of mileage to still be in perfectly serviceable condition.

Frankly, if you're not after something newer with newer tech and convenience, and you're still happy with the Mazda, the advice is probably to keep it and drive it till it will drive no further. As it is, if it's getting close to 300,000km, it's not worth very much to trade-in or sell second-hand, so keeping it and squeezing every last kilometre out of it is the budget-conscious way to go. The exception would be if a bunch of little things all go wrong at once. At which point, you're probably wise to quit it  - even though it's worth very little - as a means of not throwing good money after bad.