I don't know what the DB coaches would say, but I think sending Happy Birthday text is fine. As long as you aren't pledging your undying love saying HB to someone you spent a good deal of your life with is perfectly acceptable to me.

His email sounds a lot like what H says to me, "It might not seem it...or you may not believe me..or whatever"

You did want to move out and sell so maybe this is good. Make the decisions on your time, don't feel rushed!