The device had what seemed to me a bizarre LCD display with a controller(or microcontroller?) I have never seen before(middle image).My question is:what kind of display is this,what kind of controller&how does it all work together?Note that the LCD is attached on with the help of two rubber bands(first image) and can easily be removed or be placed back without soldering or desoldering it.Also,what's the role of the black cover placed in the middle?
The black blob is a custom IC called a "chip-on-board". The IC does not have a standard case like what we normally see when looking at a PCB. Instead, the die itself is glued to the PCB and has very fine wires coming out of it to connect to the board. The whole thing is encapsulated in the black resin to protect it from the elements.
In my experience, salvaging displays from this sort of thing is generally a lost cause--they are most often custom jobs and, while I'm sure you can find a way to reuse them, it will take a lot of time to determine the pinouts and how to control them.
It looks like the LCD is mounted to the PCB using a press-fit solution. Pressing it to the PCB connects the pads and the pins on the board and the display. By far not the best (can lead to intermittent connections if not done properly, or if the pads get dirty) but for a cheap toy it usually gets the job done.
This answer briefly explains the chip-on-board concept.