LWP::Protocol::https needs IO::Socket::SSL which needs which needs . How you install that is up to you, and if your platform has a ready-to-go package, that might be best (because if you know you don't want that, you're unlikely to ask your question).
Is it possible to perform such a request with LWP or an alternative module? I am prepared to do so with IO::Socket but would prefer something more high-level if available.
An LWP runs in the context of a single process, and there can be several LWPs per process. In addition each LWP can be running its own (user-level) thread. Multi-threaded applications are constructed by creating threads (with thread library package), and subsequently assigning each thread to an LWP.
Q2: Each LWP corresponds to a separate task (or user thread), and each is separately schedulable by the kernel. (In linux, the term "kernel thread" has a specific meaning that is quite different: a kernel thread is a thread [really task] which spends its entire life inside the kernel.
But be careful, the way LWP::UserAgent used to work, if you provide a ssl_opts hash to the constructor, then verify_hostname defaulted to 0 instead of 1. (This bug was fixed in LWP 6.03.) To be safe, always specify verify_hostname => 1 in your ssl_opts. So use LWP::UserAgent 6; should be sufficient to have server certificates validated.
When perl encounters use My::Module it goes over the elements of the built-in @INC module that contains directory names. In each directory it check if there is a subdirectory called "My" and if in that subdirectory there is a file called "Module.pm". check where LWP::Simple module is installed on your system and type below line just above the use LWP::Simple statement of your code.