Can I use SharePoint Designer 2013 to edit SharePoint 2010 sites?
Couldn't find this info in the web.
Doesn't seem so. I just tried and got the following message
Microsoft SharePoint Designer cannot be used to edit web sites on servers different from Microsoft SharePoint Server 2013. To edit these sites, you need to use the same version of SharePoint Designer which matches the version of Microsoft SharePoint Server.
Yes you can edit SP13 in SPD10! http://365.webbrewers.com/blog/Lists/Posts/Post.aspx?ID=25