Here are some of my favourite tools for web perf and analytics:
Uptimerobot.com - Free tier. 50 monitors. Sends a request every 5 minutes to a website.
Pingdom.com - Free tier. Gives average response times.
Builtwith.com - eg is this a wordpress site, what webserver etc..
Deadlinkchecker.com This handles redirects well
Command line tools
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.