I think it all depends. We found this little house we are in now and the guy never did an application on us...lol. We simply saw the For Rent sign, called him and went to talk to him. Evidently he liked the fact that we were older and "settled and non-partiers". I think he thinks we are older than we are!
Now I dont have a lot of experience with this because I havent rented anything other than this place in almost 20 years!
Depends. Most landlords run a complete credit check and rental history (although many who just own a property or two don't). Sometimes the rental history can be the hold up because you have to wait for a reply, usually via fax or email, from past landlords. That is usually what takes the longest for me to approve an applicant. If a company or past landlord is willing to answer questions over the phone, it can take as little as 24 hours.
Depends on the area, from my experience. The manager or landlord should tell you how long it will take to get an answer. We have not had it take longer than 2 days unless a weekend or holiday is involved. It cannot hurt to call and ask how much longer it will take to get an answer.