Here are some of my favourite tools for web perf and analytics:

Monitoring

Uptimerobot.com - Free tier. 50 monitors. Sends a request every 5 minutes to a website.

Pingdom.com - Free tier. Gives average response times.

Azure Application Insights

Infrastructure

Builtwith.com - eg is this a wordpress site, what webserver etc..

Deadlinkchecker.com This handles redirects well

Command line tools

Curl

Performance

Apache benchmarks load testing from the command line
JMeter and this video was a useful 10 minute guide.

YSlow for testing webpages as a browser plugin
Lighthouse Chrome extension
Webpagetest.org - scores on perf, compression, caching, CDN

Security

I found an incomplete SSL Cert security chain using: SSL Labs

Issues with security headers SecurityHeaders.com

OWASP Zed Attach Proxy (ZAP) pen testing tool for finding vulnerabilities in web apps. I’ve only briefly used this and it pointed to the same issues as SecurityHeaders.com above.

Web Accessibility

Guidelines
Lighthouse Chrome extension