hi my puppy also had blood in his poo's and the runs, but i took him to the vets and they gave him some probiotics, (protexin) and some kaogel, he was also put on hills dog food the i/d one, which cleared both the runny poo and the blood up within a week.
i would take him back to the vets as it isnt normal for them to get it. it can be a sign of a few things, busters was lucky his food was to rich. but definatly take max back to the vets. as blood isnt normal.

as for the poo's on the walks buster is 12 weeks now and he also will only go for a little number 2 on our walk if any, but he will go when he is in the garden so i think that bit just takes time for them to get used to going out for a walk and going to the toilet then and not when they are in the garden.