The reboot without warning happens if you get a popup saying restart required and you say not now. Then if you do not reboot in 30mins or so it euther reasks and if no answer reboots or reboots without asking. Did you get a popup?
That said pointing the mcafee admin here he wants the logs you have and needs to take some mer logs of your PC so they can stir the developers up. My son in law and duaghter recently saw this as well so I am getting teir logs as well. Would you be interested in helping?
The "Error code 40 / Internal error state 107" message shows that this is an SChannel (SSL Handshake) problem.
Since you haven't said what your OS is, or which version of IE you have, or what your McAfee program/version is, or whether McAfee, Windows, and other programs are up to date, or whether you have run scans with McAfee or other programs to ensure that you don't have a malware infection, then the best I can offer is some generic advice and information.
Check your Internet Explorer settings (Tools-->Internet Options-->Advanced) and go to the end. Check whether IE is using TLS and/or SSL and which versions : McAfee uses Internet Explorer settings for its operations and this may have a bearing on the messages you are seeing. In your IE Security Settings also check your Software channel permissions - are they set High, Low or Medium?
The message is commonly seen on servers and can be disabled by setting a registry value to 0. You haven't said if your machine is a server but I assume not. See the following Microsoft discussions anyway.
This error can be received due to an incompatible browser problem and SSL 3.0 connection request cannot be handled.
There may be a separate issue to do with digital certificates - a missing, expired or invalid certificate, or an encryption method not supported by a program on your system. There isn't enough information to be able to say more than "maybe".
Additional : your question has been branched to a separate thread. Please do not post a question in multiple places, please do not tack a question on to an Answered thread, and please do not hijack an old and possibly unrelated thread with a me-too post. The best thing is to ask your question in a separate thread, since your system configuration will be different from that of other posters.
As for your query about mcupdmgr : no it is not linked to any virus. I don't know where you got that idea from. It's the McAfee Update Manager.
Edit - Thread moved out of Service & Support to General Discussion