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Best settings for the contact form to ensure seamless stability:

Form name?
Action = default used with “use built-in PHP form processor script” ?
Accept charset – UTF-8 or can I leave blank?
More:
From email can be same as new? Any risk here?
To email – if “from” setting used above, can this still be $mailfrom ?
Best settings for Autoresponder? Not used typically.
Best settings for mail engine? Not used typically. When I do I use SMTP settings used in Outlook but sometimes does not work.

Misc? Anything to check other than ip address?

Which ones will cause more of an issue in not receiving a valid entry than the alternative?

There are no ‘best settings’. The reason why there are so many options is because each server/host has its own requirements.
The defaults are usually a good start. I do not recommend to change too much at once otherwise you may break more than you fix.

Specifically, is it safe to have the "from address" be the same as the "to address"?

Also, opinion on checkboxes in advanced / misc:
enable server side validation
check if domain of the specified email address is valid (mx record)

Specifically, is it safe to have the "from address" be the same as the "to address"?

It should work unless it is not allowed by the webhost, but that would highly exceptional.

The purpose of each option is documented in the help.

For example:

Enable server sided validation
This adds extra security to the form by also validating the input on the server side (using PHP), so even if JavaScript is disabled in the browser or the form has been modified (by spammers/hackers), the submitted will still be validated. This feature uses the same settings as the JavaScript (client side) validation.