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Don’t bother with the cert if it’s not your job, but at least look into CCNA Routing and Switching. There are tons of courses available, both in person and online, as well as numerous YouTube videos on the subject.
See if your local library or community college has an adult education center that provides a course. At some point, you will need to learn subnetting, which is just math, but practice makes perfect, and your life is easier if you have it committed to memory.
Proper written work is still one of the most effective ways to do this.
This is incorrect, for asymmetric (public-private) encryption. You never, ever share the private key, hence the name.
The private key is only used on your system for local decryption (someone sent a message encrypted with your public key) or for digital signature (you sign a document with your private key, which can be validated by anyone with your public key).
For the server, they are signing their handshake request with a certificate issued by a known certificate authority (aka, CA, a trusted third party). This prevents a man-in-the-middle attack, as long as you trust the CA.
The current gap is in inconsistent implementation of Organization Validation/Extended Validation (OV/EV), where an issuer will first validate that domains are legitimate for a registered business. This is to help prevent phishing domains, who will be operating with TLS, but on a near-name match domain (www.app1e.com or www.apple.zip instead of www.apple.com). Even this isn’t perfect, as business names are typically only unique within the country/province/state that issues the business license, or needed to be enforced by trademark, so at the end of the day, you still need to put some trust in the CA.