Way too young for walks near traffic at this age.
Keep it fun, make outings positive. Bring toys and treats, put him on a flexi leash so he can explore, and keep him in the yard for now.
Plenty of time for the big world out there when the puppy is older.
And I would avoid the pet store until he has had all his vaccinations.
I didn't even think about waiting till he has had all his vaccinations!