If I check in at a hotel, motel or inn at 4.00 am do I still need to check out at 11.00 am the same day ?

I would ask at the desk. I have been given a late check out , but I can't recall them giving me the whole day and night. But it can't hurt to ask. 

It depemds upon the particular facility.  Ask the front desk staff about late check-out times.

You have to ask the front desk staff at the specific hotel in question. Ask about a "daytime rate". 

There is no world wide rule on what a motel, hotel or inn MUST DO.

Open your mouth and ASK. Most places can make an arrangement for you.

They DO NOT HAVE TO.

A "Late" check out can be arranged. You ASK and be nice about it.

Front Desk may not have the authority to grant it. In that situation you deal with the management.

Depends on how full the place is and how many rooms they need for the next night to be cleaned.

Yes. The room rate is for the night, irrelevant of how long you actually stay in the room over that period. 

You do if you don't want to get charged for two nights instead of one unless the hotel has a late checkout option.

I have worked front desk. I was allowed to make such decisions. If l thought the person did not look like someone trying to take advantage, I could jiggle the computer to not charge for two days. You consider if there are 100 rooms and 25 are occupied. You are not putting-out other guests (denying a room) you are not allowing housekeeping (maid service) to do "free" or extra work, as they are not "in the room" on the housekeeping sheet; so one can play by ear. In our travels abroad, often a late or early arrival we make is accommodated by the hotel for our convenience. Tours in Turkey make a practice of letting you in at 4AM when your bus arrives and then you can rest until 9AM, breakfast, and go to the sights. THEN stay the night, one night charge. Depends on the management's strictness and desk clerk's pity!

Yes, because (1) since no one leaves before 4 a.m., they have to keep the room empty for you from the previous afternoon until 4 a.m. (they can't let someone else check in the previous afternoon because they need to keep the room empty for you), and (2) they need enough time to get the room cleaned so someone else can check in the afternoon, unless you want to pay for 2 nights.

Yep. If you dont check out by 11am, you'll have to pay for another day

if check out time is 11am then yes you have to check out the same day or pay for 2 days