I understand how the whole thing is and am not asking for the mechanism. But why has nature selected this manner instead of say, conservative or dispersive? What is the advantage of this?

Another thing as well that has really puzzled me as a biology student is, why does DNA have T and RNA have U? What happened in bases in evolution to cause this to happen? Why can DNA not have U base?

Thank you guys for any answers!

I think semiconservative replication is simply the only way it can work. Faithful DNA replication depends on hydrogen bonding between complimentary bases. That means that the original strands have to be separated at some point in the process. Therefore, a conservative or a dispersive method would both require separating the original strands and then putting them back together again. Letting the new strand and its template is simply more efficient.

As to your second question... I honestly don't know. I think it has something to do with the chemical stability of deoxy-thymidine as opposed to deoxy-uridine. Someone with a better background in biochemistry may have a better idea.

One reason I can think of why DNA has Thymine rather than Uracil is that having Uracil would increase the overall mutation rate.  That is because Cytosine (a normal DNA base) spontaneously deaminates to Uracil at a fairly high rate.  Normally, DNA repair enzymes can replace the Uracil with a Cytosine.  If Uracil were a normal DNA base, however, there would be a high mutation rate in the complementary strand of DNA of Guanine (which pairs with Cytosine) to Adenine (which pairs with Uracil or Thymine).

That's a good reason for DNA to use thymine instead of uracil, but the next question is 'why does RNA use uracil instead of thymine?'. In other words: why use uracil at all? I assume that cytosine can spontaneously deaminate into uracil in its RNA form just as easily as it can in its DNA form. That would not lead to a permanent mutation, but it would lead to mistakes in translation.

Good points above.  The origin and evolution of these molecules is quite a hot topic in evolutionary biology.  It's useful to remember that RNA preceded DNA in evolution.  As mentioned above, RNA is prone to cysteine deamination, and the 2' ribose reactive oxygen can attack phosphodiester bonds causing strand breakage.  It's thought that the first evolutionary step toward DNA from RNA came in the form of U-DNA viruses (some still exist in fact) which were relatively resistant to host RNAses.  As mentioned above, the replacement of uracil with thymine (phosphorylated uracil) in DNA allowed for the repair of deaminated cysteines. 

Briefly, according to this popular theory, RNA cells later acquired DNA and their early replicative mechanisms from these viruses.  The improved stability and replicative properties of DNA were a prerequisite for the formation of large genomes and the evolution of modern cells.  However, RNA was by no means made obsolete: DNA was a late-comer, so to speak, and RNA-based translational machinery had already evolved.