Nothing there points to a HDD failure, there's also very little way to determine if a HDD failure is imminent. The only solution is to replace it after a few years of use. However this really isn't practical and is why you should make regular backups. The HDD will fail, but it could be next week or another 5 years, and you could say that of most HDD's over 4 years old. It's a mechanical device and as such there's a lot of varying external factors that go into its current condition.
Even SSD's have their limits, although are not mechanical so easier to give an accurate lifespan on. Either way just make regular backups of important data as you should anyway, never rely on a single point of failure for anything critical.
The issues you're currently having are possibly software related, Apple would probably get you to reinstall your OS. However, given the age of the machine and you're comment on the battery I would hazard a big guess that it is the fault. The 'SMC', NVRAM or whatever are controlled by a capacitor (Normally a CMOS battery on older machines and probably still windows), this battery is what keeps the time and stuff. If your battery is faulty (And at 6 years it's more than likely) then there could be an issue in this capacitor receiving a charge or failing somewhere.
So if moneys tight (Which I'm guessing it is if you're looking at a 2013 model) then I'd suggest you replace the battery, you could even just open it up and check it for physical signs of age (If it looks swelled then replace immediately). This should only be about $70 and will likely solve the problem.
If you are dead set on a new MBP then a 2013 would be fine, there is no better or worse model available, just get the newest one you can afford really. However I'd note that it wouldn't be exceptionally better than your current model, and may still have battery issues given that it's still an older machine.
Hope that helps! Back up your data and consider swapping the battery.
