(1) Yes (2) Yes and (3) Yes.
The only conceivable downside is that you will miss some flying days because of winds that are acceptable for spamcans but no good for Tiger Moths, but PPL training in the UK invariably involves lots of hanging around and cancelled sorties and, as you have said, you are not in a hurry. As you probably know, if you learn on the DH 82, you have to do the IMC familiarisation bit of the course in a PA 28 anyway, so you will get to see what you are (not) missing.
If you send a private message to Tiger_Moth he might recount to you his adventures in achieving a PPL from scratch on the Cambridge Tiger Moths.
Have fun.