DNA sequencing problem
Even though you - or the problem did not clarify, I assume in my answer that you work with eukaryote system, even though the principle of the replication is the same.

dNTPs do have an OH group on their 3rd carbon atom (for eg. check this wiki-page for dCTP) so I don't think that's the issue here. My guess is that the first tube contains the radio labeled GTP and the second does not, so even the DNA is there, you cannot see it - even though the question specifically asked why DNA was not synthesized, my opinion is that it's a tricky question to confuse you.

For the second problem we need to dig into the replication process a little bit:

In the replication fork the two strands are synthesized differently. The so called leading strand is made continuously, without interruptions, however the other strand - the so called lagging strand is synthesized by ligating small fragments - aka Okazaki fragments. These small fragments require their own RNA primers that need to be removed after synthesis is done.
Now since the origin of replication is in the middle and replication can proceed both ways, on a linear fragment such as yours you can get two 2000bp fragment from the two leading strands. Would it be a circular DNA, then you could still get 4kbp fragments since the replication could go around the DNA circle.
The smaller 500bp fragments that are quite abundant in the tsr1 lane, are the fragments that cannot be ligated. That being said I must admit that 500bp Okazaki-fragments would by atypical for eukaryotes (usual is around 100-200bp). So the enzymes responsible for this could be:

DNA Ligase - the one responsible for ligating (joining ) the lagging strand's fragments.
Polymerase delta (Pol δ): That is responsible for lagging strand synthesis and primer removal - in this case the primer removal function might be defective, this causes that the primers stay on the DNA and complete synthesis and ligation cannot occur.
The last protein although it is not quite an enzyme is the DNA clamp complex (PCNA). This complex stabilizes the polymerase to DNA, but when reaching a previous fragment the polymerase should dissociate. But if the clamp is dysfunctional than the polymerase gets stuck on the end of the fragment thus no primer removal and ligation can occur.

If need more info read this wiki-page.