Many do, but it is always worth checking the description as some only have a small outdoor space or are on the first floor, perhaps with a balcony. This can be fine with a small dog, but an enclosed garden would be better if you own a large breed.
Lots of properties offer accommodation suitable for disabled guests, such as ground floor wet rooms and bedrooms. However, there may be steps accessing the property, so it’s always worth checking first.
Yes, definitely, there are some dog friendly pubs and cafes in the town and the South Tynedale Railway is an award-winning pooch welcoming attraction.