When DNA is replicating, how can the polymerase add so many bases so fast? Where does she get them?

The bases are just floating around in solution, and occasionally collide with the polymerase. At the small scales, molecules move much faster than you might think.

The nucleotides hang around. Not the pure bases. Also remember that the volume is rather low.

Well, I could have called them deoxyribonucleotide triphosphates but didn't feel like it. Incidentally, two of the phosphates are removed to provide energy, just like ATP. Edit: As CharonY said, it's like but not the same as ATP, I forgot about the extra deoxy bit.

Edited October 7, 200916 yr by Mr Skeptic
oops

Not quite, for DNA synthesis deoxy-ATP (and the respective other nucleotides) is used. Also ATP-dependent energy transfer is normally limited to a single phosphate residue (i.e. from ATP to ADP). Whereas during DNA polymerization PPi is removed. But yes, the principle is very similar.

Edited October 7, 200916 yr by CharonY

Ok. Is the transport from cytoplasma to nucleus work of enyzmes? Is the transport of nucleotides to cell connected with the needs of cells?

The nucleus possesses porins (essentially proteins that form a channel) that are large enough to let nucleotides pass. IIRC there was no difference in nucleotide concentration between between nucleus and cytoplasma, further indicating free diffusion.