HTTPS does not work at 100% and automatic site loading as HTTPS.

1. The Web is loading as HTTP.

The problem is that it is not enough just to activate HTTPS, but it is still necessary to change the WordPress settings. Specifically, Settings -> General and there change the WordPress Address and Side Address to HTTPS.

The site is loading HTTP because WordPress the current setting tells WordPress to load HTTP. WordPress doesn’t know your site has HTTPS.

As it turns out, you can’t have your cake and eat it too. If you want your site to load with HTTPS, you need to tell WordPress as such.

However, what happens when the certificate ends?

If your certificate expires, visiting your website will show an invalid certificate warning in the browser.

If you don’t want that to happen, you renew your certificate when it expires. In fact, you want to renew it BEFORE it expires.

Better yet, use a host that will automatically procure, install and renew your certificates for you. The bar for HTTPS/SSL is so low now that even el-cheapo $2/month shared hosting companies offer free, unlimited and fully automated SSL certificates. That’s because it’s built into their control panels and the cost to them is zero.

If your host doesn’t do this for you automatically and for free, it might be time to go shopping.

If you really cannot renew your SSL certificate and can’t use a host that does it for you automatically, then the only choice left is to NOT use HTTPS.

2. When I log in to /wp-admin, it will appear that the connection to the site is not fully secure. The second site works fine, so why does it work badly here?

What is the second site? I ask so I can compare the two.

In any case, before troubleshooting any further, you want to switch your WordPress URL to HTTPS and ENFORCE SSL (ie, automatically forward all HTTP requests to their HTTPS equivalents at the server level).

That is, if you want HTTPS to work properly on your site and not see any browser warnings.

Good luck!