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.

wget requires openssl

so make sure you have openssl installed on your homebrew system

$ brew list | grep ssl
openssl
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If openssl is not installed then install it using "brew install openssl"