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Your car is still under warranty, so take it back to your dealer and request that they investigate the cause of the surge and rectify it.
They are very different cars, the Viva is small, the Falcon big, so it comes down to what you want from them. The Viva is newer and will have done fewer kilometres, the Falcon is getting old and is likely to have done lots of kilometres. That said, Falcons tend to be relatively reliable at high kilometres, so if you are after reliability that's probably the better bet for you.
Mitsubishi has recalled a number of 2015 and 2016 models in North America for a hesitation problem with the CVT. The problem is a slow response when accelerating. But overall the CVT seems to be quite reliable in the Lancer.
I would get a second opinion on the Kia's engine before you do anything else. A sludged-up engine suggests a lack of servicing, but if no damage has occurred you might be able to salvage it. I wouldn't recommend either a Multivan or Valente, those you are looking at are too old and potentially too expensive to run and repair. A seven-seat SUV might be a better option.
I think you've done well to get that deal. The problem you now have with the engine could well have started with the earlier thermostat problem, so getting a deal to fix the engine now at a modest cost is a good outcome.
Does it crank over when you turn the key? If it doesn't I would suspect a problem with the cam timing chains that has caused serious internal damage. If it cranks over, but doesn't fire I would be looking at an engine sensor that has failed. Take it to a dealer and have them check it on their diagnostic gear.
The price is on the high side, but the kays are below the average for that model. There have been problems reported relating to cam timing belt failures that have led to major engine damage. I would avoid early Amaroks like the one you are considering and go for a safer option of a Hilux, Navara, Triton etc. rather than tale the risk.
It's hard to know exactly what you want to know, but briefly the Trendline is the entry level model, the Comfortline the mid-range model, and the Highline is the one with all the gear. The list of standard equipment increases with each model.
You first need to decide the level of off-roading you will be doing because that will determine if you need a four-wheel drive or you only need an all-wheel drive SUV. From what you have told us I suspect that an SUV, such as a Kia Sorento, Toyota Kluger, or a Nissan X-Trail would be the best all-round vehicle for you. All of those would fit your budget, they will all go off-road to a reasonable degree, and they're all reliable. The Mitsubishi Triton is a hard-riding ute, which I don't think is what you want, but the Suzuki Grand Vitara is a good vehicle and would also fit your needs.
Basically the drivetrain is biased towards economy when Eco is selected, so you get better fuel consumption. When you select Sports mode you get better performance and will lose a little economy.