When the vesicle is swallowed of course the lipid layer internalizes. My question is how will the top segment of membrane will bind back together when that vesicle took the membrane with it inside cytoplasm. Will the plasma of the cell decrease or they will repair back and how does the membrane know that a certain substance is outside and i have to internalize myself in order to swallow. The same thing with exocytosis: How does the membrane open itself and repair back and what will happen to the membrane of the vesicle which went out?
You have one misconception about the endocytosis: In the process no hole in the membrane is generated. It works in principle like in the figure below (it is of course more complicated, but this should explain it):
The membrane forms a vesicle around the particle which shall be integrated until it is completely surrounded by a membrane. At this point the vesicle is detached from the cell membrane and inside the cell. To accomplish internalization, the particle binds to certain receptors which regulate this process. See the Wikipedia for more details.
Exocytosis works in principle the other way round. Here are the visicles detached from the Golgi apparatus (mostly at least) and are directed to the cell membrane. Here the fuse with the membrane and form a pit which has its opening to the outside, releasing what was in the vesicle. It works like this (image from here):
In this process you have to differentiate between permanent unregulated exocytosis and regulated endocytosis (for example for the release of hormones) which are regulated by signal transduction pathways.