wget unable to download anything from https sources.
It would appear that your issues with openssl are indeed the cause. From the wget manpage:

HTTPS (SSL/TLS) Options
To support encrypted HTTP (HTTPS) downloads,
Wget must be compiled with an external SSL library. The current
default is GnuTLS.  In addition, Wget also supports HSTS (HTTP Strict
TransportSecurity).  If Wget is compiled without SSL support, none of
these options are available.