how do i add a new lead source

You need to create the field and values in the Field Management area in the Admin section. Once that's created, you can click the "+" on your form and search the field name to add to your form.

Sure, just add the value you want.

You may need to look at SFDC to add that value to the picklist though.

How do I create that field in Marketo's Field Management? And how do I ensure that it shows up on salesforce? (i already have the marketo/sfdc sync working)

Thanks

Here is a link to how the create custom fields in Marketo. https://community.marketo.com/MarketoArticle?id=kA050000000KypGCAS

If you want the field to sync with Salesforce, you need to create the same custom field in your Salesforce instance.

How do I hide this field from the people that are filling out my form?
It won't let me hide it unless I put a condition on it