Is Hop up Feeder a mandatory component?
 

http://shop.ehobbyasia.com/media/cat...-M4_1_mark.jpg

Are all receivers requires the installation of a hop up feeder? Is it possible that some receivers may not require hop up feeder at all?

all plastic bodies need that
metal bodies need one piece hopups with that part built in

some use a one piece hop up those would not need that piece, some use a 2 piece, which would need that piece depends on brand reciever

Only if you like guns that dont feed. Assuming you have a plastic body.

To reiterate what has been said so far in regards to the image you have linked.

Stock TokyoMarui armalites come with a 2 pieces hopup system. The pic you have link is the lower half of the unit that allows feeding from the magazine into the secondary part of the hopup device.

In other AEGS were the receiver is separated by sliding the two portions apart only a single full metal hopup unit is required. That single metal unit is seamless combination of a two piece unit.

So to answer your question, yes one is required if the M4 style AEG uses a 2 piece hopup unit

No, check out what you have before buying and it doesnt matter
if its a plastic receiver or plastic hop up. Ex. Ics has a plastic hop up for m4 and its one piece. JG m4s with plastic receiver has one piece metal hop up. So check what you have before buying.