This is without checking, but I think the answer to both is 24 Squadron. As far as I am aware, it has unbroken continuous service since 1918, unless you count the minute between the disbandment of the original 24 Sqn in 1920 and the formation of the new 24 Sqn the same day. The only Bloodhound associated with that squadron is going to have been of the canine variety.
(If you're wondering about the minute, the form is normally that a unit officially disbands at 23:59:59 and reforms at its new location at 00:01:00 the next day.