Thanks for the explanations!
First your second problem :), gmail’s SMTP server is rejecting your credentials. The link it provides you (https://support.google.com/mail/answer/78754) tells you to use an “app password” or to set your google account to allow “less secure apps”.
If you don’t do that, then you can’t use google’s SMTP server, unless you use a client (in your case, whatever Wordpress uses) that is updated to work with “modern” Google requirements.
As to your first problem, which relates to my question regarding “information about your website”, it depends on how your website is done, i.e. how it sends e-mails. You mentioned Wordpress, but not how your website sends e-mails (check How to send e-mail in WordPress, where they mention various possibilities).
If you have configured Wordpress (and/or whatever plugin you’ve installed for sending e-mails) to use your gmail account, then you have the same problem as your second problem: Google doesn’t allow authenticating with username/password, unless you allow “less secure apps” or generate an “app password”.
Normally you would install your own mail server rather than using Google or some other freemail provider. But this is way out of scope here, and I’d suggest you look for a professional to install/administer it, as the world doesn’t need yet-another insecure mail server (no offense intended, but it’s not a trivial thing to do/maintain).
Maybe as a first “workaround”, just make an account with some other (free) provider, and use that one instead of Google. (I’d also avoid Outlook/Hotmail/etc. as they may also have non-standard requirements).