Wrt the first error, it's possible that your webserver is mistakenly trying to speak unencrypted HTTP to a request that came in on port 443 (HTTPS).
To test this, telnet to port 443 on your webserver's hostname or IP address and issue: GET / HTTP/1.0. Assuming the IP address is 10.0.0.1, that you're using Windows, and that you have the Windows telnet client installed (which sucks, btw - I prefer SecureCRT or PuTTY, which is free), type the following in a command prompt window and press Enter:
telnet 10.0.0.1 443
When the connection is established (you should see a blank screen with a blinking cursor), type:
GET / HTTP/1.0
...and press Enter twice.
Quick note: You won't be able to see the stuff that you type after the telnet session has been established, even though your keystrokes will still be sent to server. In the Windows telnet client, a setting called "localecho" controls this behaviour, but it's turned off by default.
Quick note #2: Backspace "won't work", so be careful not to make a typo or you'll need to start from scratch.
If you get back plaintext, readable HTML, you probably have some problem with your virtual hosts configuration.
I'm not sure about the second error, though, and even if the above is the case, it shouldn't cause Apache to gracefully restart...
Best Answer
That looks like someone trying to connect using SSL to a non-SSL port (i.e. https://).
Either the connecting clients are getting something wrong, or perhaps your web server is listening on port 443, but not for SSL connections?
You could create an Apache
customlogusing%psomewhere in the output, and track which port those connections are actually turning up on. If they're on port 443 then your config is potentially the issue, if they're on port 80, I'm not sure what to suggest.