as long as you operate them within spec heat isn't an issue for a sub.
i can't promise a sub won't blow out ever but there are plenty of options out there with long term proven durability in general.
about the only thing that dictates how expensive an install is going to be is how much you want to install.
for example once you install an amplifier and subwoofer that is pretty loud you are forced to purchase better highs/mids and amp them to keep it balanced.
battery location is a bit of a non issue with proper wiring done. big 3 upgrade, alternator that can keep up with the power drain, large gauge wiring to prevent bottlenecks are going to be more relevant than the batteries location.
being in the trunk actually does little more than force some extra work tbh. you'll be replacing every bit of wire from the alternator to the battery and then running wires from the batter to the amplifier.
now onto the items you linked: the icon series is good but keep in mind those subs come with a 3 week+ build time estimate.
x series more for loudness oriented than sound quality so no not a very good choice for what he wants.
the SQ model is okay, but i'm not 100% on it being the right option here.
there are just a lot of options when you have money a good budget it will just come down to personal preference.
for example i can't force him to go with 1 sub over 2 if that makes him feel more comfortable. there are merits to it like if one blows out down the line you can just rewire the one you have left and use it alone.
it's gonna be around $700 for a gps head unit alone to give you a bit of perspective.
a couple good sets of components with be around $300
subwoofer prices will vary. figure $400 or so to fit his needs.
amplifier for sub(s) $300-500
amplifer for components probably $200-300
wiring altogether around $100-150
maybe $100 in sound deadening material
$100-200 on the box for the subs.
on your end it's a good plan for you guys to start checking local shops for custom ported box prices. prebuilts are okay but custom will let you have your choice in box tuning.
keep in mind that budget does not cover a high output alternator which you should figure $500 to be safe.
http://store.soundsolutionsaudio.com/products/08-10-chrysler-300-240a-high-output-alternator.html for example would work.