Good day, madam,
fruitkiller wrote:So what is one to do (a higher kernel means being able to install higher versions of certain software is my understanding, tell me if I'm wrong).
Mostly a newer kernel means better hardware support. If all is going well with your machine right now, you do not experience crashes or freezes, and all your hardware is supported, a newer kernel will not bring you any noticeable advantages. If there are no problems to solve, you don't need to upgrade your kernel.
So before you ask: How to upgrade my kernel
, the question to ask is: Why to upgrade my kernel
fruitkiller wrote: the system does not seem to want me to particularly do so (not appearing in the updates ever, and I have all 5 levels of updates allowed to appear.)
From my understanding, and I too may be wrong, in Mint 17.X newer kernels are not shown as an update, no matter which levels you have made visible.
By the way, it's better to start your own thread for a new question. This one is pretty old and part of it is very outdated.