I can't understand why the electron is slowed/stopped by the nucleus.
The electron is a negative charge and the nucleus is positive... they should attract each other...
Bremsstrahlung radiation occurs when a charged particle (like an electron) is deflected by another charged particle, or charged object (like a positive nucleus). The electron does not have to be stopped, or even slowed down for this to occur. Simply deflected.
An electron moving quickly passing a point of opposite charge (positive nucleus) will, as you said, be attracted by the point. It therefore feels a force and will be accelerated towards the point. Of course it already had significant momentum so the net effect is to slightly change the direction of the electron.
Any time a charged particle is accelerated/decelerated/deflected it emits radiation.
Now Bremsstrahlung radiation is mostly associated with energetic electrons being absorbed by matter. In this case, there are huge numbers of nuclei. The interaction I described above will occur many times deflecting the electron randomly each time, and each time some radiation will be emitted. The net effect of this is that the electron loses energy (as electromagnetic waves, light) while also losing any sense of direction.
Eventually all initial kinetic energy the electron had initially has been dissipated as radiation.
Aside: When protons (positively charged particles) go round the circle of the LHC, they emit high levels of EM radiation simply due to the magnets constantly deflecting them. Standing in the tube while the LHC is running would result in a very quick death by gamma radiation :)
The nucleus field attracts the electron when the latter is approaching the former, but it attracts the electron either while the electron is behind the nucleus, so the net effect of interaction is zero providing the nucleus does not move and there is no inelastic losses. Bremsstrahlung is an inelastic loss of energy-momentum. In addition, the nucleus gets some energy-momentum from the electron (it gets a push), so the net effect of interaction is stopping the electron.