APSDaemon is part of "Apple Push". If you feel you need Apple Push then I would try reinstalling it.
As for your gmail only showing secure messages, are you sure it is not just a prompt that some of the information is not secure? Normally this would be related to browser settings. Choices for displaying mixed content are
Disable, will not display non-secure items.
Enable, will always display non-secure items without asking
Prompt, will prompt you when a webpage is using non-secure content
The default is Prompt. So normally you just say OK to displaying the insecure data and then you see it all. You can change the setting to Enable but Microsoft doesn't recommend it.
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