Does WebHelpDesk 12.1.0 support Exchange 2007?
Yes it does but you will need to use POP3 or IMAP as your incoming source. For outgoing it is simply SMTP.
Exchange 2010/2013 can use Exchange Web Services which is a much better way of allowing an incoming source.
Exchange 2007 goes EOL in 2017 and if you can I would look to use this as another reason to move to 2013 as soon as you can.
You can use EWS on 2007, just make sure you enable digest authentication on the EWS site in IIS on the Exchange server.
It does but I'm not sure if WHD uses the 2007 methods/properties as the documentation says Exchange 2010/2013.
It uses the same connectivity method (EWS) as 2010 / 2013, although one thing to keep an eye out for is the certificate being
on the Exchange server, if it is SHA256 signed then WHD will not be able to connect to it no matter what version unless you upgrade
the WHD Java to Java 7 or install the release candidate which uses Java 7 natively
