As touched on - the fallow are centred on Raehills (from where, I gather they escaped from the park some year back) near St Ann's and have spread in all directions from there apart from east (they haven't crossed the M74) so: yes in Annandale but only west of the M74 and no to Lockerbie.
As for the sika they are certainly more plentiful east of the M74 and are shot on sight on many lands west of it to try and protect the integrity of the red deer in Galloway. The FC set up a red deer conservation area to the east of the forest to try and further enforce that. The M74 helps for sure. I have seen sika and hybrids shot west of the big road over the past 25 years but it does seem to be diminishing in my experience.
From memory the study done towards the end of the last century proved that there was, indeed very few pure red deer in Scotland, the exception being on some of the more outlying Hebridean islands including Rum.