You're driving that car in what's called "extreme service". As mentioned, the oil never heats up which is actually great for the oil but it's a ^%$#^%& nightmare for everything it touches. The engine never gets to operating temperature, or if it does, only briefly so the bores, valve gear and other 'round bits in tight spots' never operate as they should.
I'd change it every 6 months, without fail. Regular oil of the right grade, a 'name' brand and whatever's cheapest will do if you're going to do it yourself. Filter, once a year will be fine.
I actually bought a 'disposable car' to take those trips off the new car we got last year. She's adopted it as her own unless the trip is longer than 15 minutes and/or she's taking the kids out and/or she needs to carry our kids and a few others. The disposable car has 150,000km, the engine sounds like a tractor and pulls like one too (660cc! With turbo and every bit of 10 year old Mitsubishi gizmosity they could throw at it). If the electric version of the car was double what the dispo car cost, I would have got one of them as electric is made for that kind of work.
The new car, gets it's service every 5,000km, which is every 6 months. Service contract, the dealer collects it, does the work, brings it back. The dealer is a good one and all I need to is stick fuel in it, of which it doesn't need much.
As far as fuel goes, that's something that's kind of "suck it and see" really.
Cheap fuel and good enough for the engine is fine. Really. It's fine. Higher octane fuel might have more cleaning stuff in it, but the detergent package is likely in 'good' quality regular already. I stick regular in the dispo car, high octane in the new car.
The dispo car is happy on regular. The new car can and does take full advantage of the high octane fuel, even though it's 'safe' and 'recommended' to run on regular. The cost difference between the two means hi octane needs to get 8% better fuel economy than regular to justify it cost wise, which it does easily. And the car is much happier on the high octane. When you manage to have the car regularly get the same fuel economy the advertising says it should, it's a shock. Our old Mazda never managed to do that, even on the highway.
But again, suck it and see. If higher octane works, use it.
Honda generally make good engines but if you're being hard on the engine and don't try and help it, it's not going to like it no matter who made it.
Or you could simply drive it into the ground. Folks here do it all the time. I can't do that myself, so I try and take care of them.