For the sake of simplicity, I'll use "screen" to mean the final surface we'd take measurements from, and "wall" as the thing with the slits in.
Could some electrons just get lost or go through the wall between slits?
Not realistically, no.
Assuming that all of the emitted electrons will either hit the wall or the screen, I don't see any way for electrons to be "lost"*. The chances of an electron passing through the screen somehow (eg. via quantum tunnelling) are vanishingly small as the screen's thickness is relatively very large.
*In reality, electrons might fall short due to interactions with air or dust, or they might miss entirely!
If [the wall] has a thickness, could an electron hit the side of the slit?
Of course! Hopefully though, the equipment would be set up in such a way that the chance of this is minimised. Any impacts of this kind would be counted the same as electrons impacting the wall in the normal (heh...) way.
Would the [total] number of electrons [observed impacting the screen OR the wall] be the same [as the number emitted]?
Yes! Taking from above that no electrons are "lost", then all the emitted electrons will either impact the screen or the wall.
Recently (as "recently" as Christmas 2012) a series of brilliant animations have popped up on Wikipedia. This one in particular (or is that wave-ular...?), as seen on the Wave-Particle Duality page gives a really concise demonstration of the double slit experiment with electrons.
As described in the animation, the emitted electrons behave as a wave right up until they interact with something, in this case the screen or wall, and the interactions we see on the screen (not the wall) follow the same diffraction pattern as that of light in a similar set-up.
The key thing to take from the animation is that the amplitude of the diffraction pattern (for light, the brighter and darker lines or "fringes") dictates the likelihood of electron impacts and NOT where somehow some electrons are more energetic and others are magically lost to the aether.
Are all electrons going through the slits?
If the electron gun is directed between two slits, than [shouldn't the electrons all] hit the central part between the slits?
NO! It's easy to imagine emitted electrons as all following the same perfectly straight path from gun to wall, but in reality things usually don't actually behave that way.
Here are a couple of nice pictures I found: [One], [Two]
There is always going to be some divergence in the emitted electrons. Besides, what would be the point of the experiment if you made sure all the electrons were hitting the wall?