I believe the Edit button in the Multi-File Find and Replace is simply launching the default editor. To confirm this, try performing a similar action using Windows Explorer. Right-click an HTML file and choose Edit from the context menu. You will likely find the same behavior.
If you wish to change what application opens, you can try modifying your Windows Registry as described in the link below:
Sorry, but I cannot help on the issue with help not opening the proper context sensitive topic. That's in Adobe's realm.
For both issues, I would encourage you to submit a Wish Form/Bug Report to ask Adobe to make changes with the way this works.
Helpful and Handy Links
It is the default editor for IE that determines what is used and you may find your chosen editor is already listed there. If so, just change it.
If it is not listed and you are not comfortable editing the registry, you can download a utility from http://windowsxp.mvps.org/htmleditor.htm that will make the change for you.
See www.grainge.org for RoboHelp and Authoring tips