Your TBBs that rely on the TOM.NET API should be fine. There are a few deprecated methods mostly around Filters, but they are only deprecated and should still work in Tridion 2013.
Your Custom DWT Function Sources should also be fine as they rely on TOM.NET.
Anything that relies on TOM/TDSE, including Workflow and Custom Pages will require a Legacy Pack installed for Tridion 2013.
Your UI extensions will need to be completely re-written, as a new framework has been introduced for this with Tridion 2011.
You will need to upgrade SiteEdit to Experience Manager, but any SiteEdit markup you used in a DWT template remains the same. In case you were using the SiteEdit TBBs, then you will need to replace them with the new XPM versions.