[cygx]

at the edge of it expansion of space pushes stuff outside faster than speed of light

Not quite: According to the cosmological standard model, the visible universe will continue to grow (ie new galaxies will continue to come into view) - but only asymptotically, ie until a maximum size given by the comological event horizon is reached. However, the parts of the universe that aren't gravitationally bound to us will become fainter and fainter and increasingly resdhifted, and eventually, we'll be unable to detect other theoretically visible galaxies due to technological limitations.

[ajuc]

If they are moving away from us faster than speed of light because of expansion of space - wouldn't it mean at some point no new light from them reaches us? Even ignoring the limitation of equipment?

[cygx]

In my opinion, that whole 'moving away from us faster than c' business is not really a good way to think about this: For one, we can see to a redshift of about 10, corresponding to a comoving distance of about 30Gly, and a recession velocity of about 4c (four times the speed of light!) at time of emission.

There's a cosmological event horizon. Light emitted from within will reach us in finite time, light emitted from without won't. Similar to how a distant observer will never see on object falling into a (stationary) black hole cross the Schwarzschild horizon, we won't see galaxies crossing the cosmological horizon.