Generally speaking, NO with some exceptions.
Yes, there are designated stroller parking areaas. There are usually CM's at these areas neatening up the lines and making more room so your stroller may be moved within the same area after you leave it. Don't panic if its not in exactly the same place when you return.
Some restaurants will allow a stroller if a young child/baby is asleep others won't. It seems to depend on the layout of the restaurant and how busy it is a the time.
No strollers allowed in lines/queues and in some of the pavilions esp at Epcot.
Definately not at BBB its very congested inside anyway.
If you have a baby/young toddler I would highly recommend using a sling/bjorn in addition to the stroller. When my dd was young it was a lifesaver in lines and pavilions where the stroller isn't allowed.
TJ