Creating Ajax backend for Specialised Page Template? Should admin-ajax.php be used?

We’re scoping an upcoming project that will require the development of a large php web application within an existing wordpress site – this is for our use only and we’ve no intention of trying to package it for other users; so interoperability isn’t really a concern as long as we can continue to apply WordPress updates as they’re released without breaking our application.

Update jquery version

I run WordPress version 4.7.2. and it uses jQuery version 1.12. I need to update this version to a higher one. I replaced it with a new version before, but when I upgrade WordPress core it is replaced with 1.12 again.
How can I change the version of jQuery that WordPress uses permanently?