Would it be worth me installing a water softening filter to avoid wear and tear in the future? I don't mind drinking or washing with the hard water, but if it makes sense to prevent premature damage to another water heater, washer, furnace humidifier, etc I might do it.
Between hard water and 10 years, it's possible that your water heater is filling up with crud. Depending on where the temperature sensor is located, the gas might just be heating up the crud layer instead of heating up the entire tank.
http://www.familyhandyman.com/plumbing/water-heater/how-to-fix-a-water-heater-pilot-light/view-all (troubleshooting)
A water conditioner is absolutely a good idea and well worth your time. We have a gas water heater going on 17 years and doing great, in no small part due to the water conditioner that's also going on 17 years (and also doing great). The water conditioner will also reduce the mineral deposits around sinks, tubs, showers, and toilets-- less cleaning required.
I'm checking our rental's water heater anode rod next week. When you buy your new water heater it's worth your time to unscrew its anode rod, wrap some teflon tape around the threads, and reinstall it. If the water heater is going in a room with an eight-foot ceiling and the anode rod is a cheap single piece of straight metal, then it's also worth replacing it with a flexible anode rod made up of smaller segments.
You definitely want a strap. You may also want a leak pan with a gravity drain in case the water heater (or a valve) springs a leak.
http://www.familyhandyman.com/plumbing/water-heater/replacing-a-water-heater/view-allhttp://www.familyhandyman.com/plumbing/water-heater/extend-the-life-of-your-water-heater-by-replacing-the-anode-rod/view-allIf it's tough to get at the parts to solder them, you could try a solderless fitting like Sharkbite or Gatorbite. I've never used PEX for a water heater installation but I've read many plumbers raving about its convenience.
Check your local utility and govt regs to see if you get a rebate for an EnergyStar high-efficiency water heater. Even if there's no cash incentives, the high-efficiency heaters are generally made with better components. You'll also save a little money on gas, although it's a pretty lengthy payback.
I should clarify: I've heard second-hand of states that require a tech to do the installation, otherwise you won't be able to sell the house. I have no idea if this is true or not, but it's worth looking into. It might be something like insurance companies or mortgage lenders will require it to be fixed, and not actually a legal/regulatory thing.
Um, no.
If a buyer knows the code (or hires a home inspector to check) then they may hold up the sale until the code issue is corrected (or at least compensated). But there are no insurance companies or mortgage lenders who will bother to check this, even if it's a free service from the gas company. They might hold the homeowner liable if the out-of-compliance equipment causes property damage leading to a claim, but there are no authorities that will keep you from selling a house because of a DIY repair.