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I'm not sure about your statement of "In Office 365 you cannot use SharePoint designer..." SPD is immediately available from the Site Actions dropdown, unless you're speaking about a specific scenario where SPD cannot be used.
You may also want to check out the SharePoint Online Developer Resource Center if you haven't already:
The public web site has the same custom stylesheet option as OLSB had. But I agree with you some clarification is needed on whether or not SPD can be used to create public pages. In fact some clarification on the whole Sharepoint/public issue is probably more pressing than information on team sites, since that's likely going to be used a lot more than team sites.
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I'm no expert, but have used some CSS with OLSB (works the same in O365). You can access the default CSS for a starting point, there is a link to it in the Style Sheet, just above where you enter the code.
I created the following guide for OLSB and most of classes seem to still be the same. coderightdesign.com/.../CSS_Guide_OLSB.pdf
I have also created some OLSB custom themes that can jump start your design: coderightdesign.com/themes.aspx
Hope that helps!