Well let's start with Rainmeter.
It should not create for any conflict
These are two completely independent programs, and Rainmeter is so simple in its implementation that it should not really create a conflict with anything, or at least nothing to date has come up at the Rainmeter Forums or here.
ok; F1 alone, is "hooked" to most programs "Help"
Therefore; Circle Dock has a two-key Hotkey set up.
F1 alone should not do anything with Circle Dock (if it does, please let us know)
That being said, I am sure that you have come across the assignment options in the settings.
In the "Visibility" tab:
As you can see I have mine set for Ctrl+F1. This has been a champ for me, as I use a mouse that I have assigned a button to handle Circle Dock visibility.
If this is not working for you, please advise, and we can have a closer look
I am going to add the start menu issue to the list as it maybe related to an issue I am experiencing as well.
In my case I open the start menu, and it "snaps" back to the taskbar.
Very annoying, so your case must be most frustrating
That toggle button has created for more issues than it has been worth and may be removed at some point in the future, as it's use also creates for other visual and user issues
If anything I have just posted has not helped. let me know and I will work with you to get as many issues resolved as possible