Forms

Hi Colleen.
First thing to ask yourself, is this a brand new Marketo instance? Or are you coming as a new user to an existing instance.

Nothing you describe is "out of the box"  functionality. You need to write a smart campaign to do each thing you describe. But to be frank I don't even quite understand some of the things you say.

1. When someone fills out a form, that data goes to their lead activity log. You can find all the people who filled out a particular form by creating a smart list using the filter "filled out form" is "form name". 
2. New Leads who fill out a form will only sync directly to salesforce.com if you've written a smart campaign to do so. There is no "via" a field, nothing to do with Lead Source. You can write a smart campaign which says Fills out Form, Change data value Lead Source to Form Name and Sync Lead with SFDC. But you have to write that logic, it doesn't automagically happen.
3. Lead Source is ONLY the first place a lead comes from, in my book. I never overwrite Lead Source. In Admin you can block a field from being updated once it has been filled out once. I have that set for Lead Source & Lead Source Detail.
4. Fields like Lead Source should be mapped to both the Lead & Contact entity in SFDC and will sync with Marketo's Lead Source. But that data shouldn't be updated.
5. Use "Interesting Moments"  to reveal things like "Filled out Form" names in SFDC. Don't use a static field, you'll end up using up all your API calls in a day and having data issues. 

I hope this helped, but I'd really recommend starting from the beginning and really learning what's going on before you just start doing. If you've noticed on the right side, Marketo has 2 "freel learning days" where their paid courses are free. January 2nd & 3rd. Take the time over those two days and really learn how to operate the system. 

http://community.marketo.com/MarketoDiscussionDetail?id=90650000000PjkeAAC