proteins - DNA Replication - Biology

I think that you have a couple of points wrong. Since your question is asked using bacterial terminology, I'll stick to that.

The leading strand, the one that is initiated at the origin of replication, is synthesised by pol III which is a highly processive polymerase, i.e. it keeps on going for long periods, making very long products. In principle a single pol III molecule could produce the entire leading strand copy of the template.

The lagging strand is, as you say, initiated at multiple RNA primers. The enzyme that extends these primers is pol I. As polI extends a primer it creates an Okazaki fragment (i.e. this is not an alternative name for the primer itself). Eventually the pol I will encounter the 5' end of another RNA primer. At this point the 5'>3' exonuclease activity of the pol I comes into play and removes the primer, replacing it with DNA. The pol I will probably also degrade some of the DNA that has been added to that primer by another pol I, resynthesising it as it goes. This is so-called "nick tranlation" since as the pol I moves along the template it moves a nick in the new strand as it goes. pol I is not a very processive enzyme however and will fall off, leaving the nick to be sealed by DNA ligase.

The leading strand does require a primer, and in most cases this is an RNA laid down by the initiation complex at the origin of replication. In some cases, a protein provides an -OH group for DNA polymerase to initiate at.

human biology - At what age do babies begin to synthesize their own antibodies?

In the graph above the darker blue line refers to the antibodies the baby receives from the mother in utero, as you mentioned in your question.

As you can see, the red line indicates that babies begin to produce low levels of their own antibodies between 3 and 6 months before birth. However, these are IgM antibodies, immature 'rough draft' versions. These have much lower affinity for antigens then their mature IgG counterparts which are the classically thought of antibody.

Levels of an infant's own IgG start to rise after birth, however don't reach a reasonable level until after the child is roughly 1 year old. Maternal antibodies start to tail off at around 3 months leaving a period highlighted in blue on the graph where infants are particularly prone to getting infections.

organic chemistry - Saturated vs Unsaturated Fats -- Structure in Relation to Room Temperature State?

In the solid state the individual triacylglycerol molecules are interacting with each other primarily through Van der Waals interaction. These weak bonds between molecules are broken at the solid-liquid transition. The amount of energy needed to disrupt these interactions (which determines the melting point of the fat or oil) is determined by the energy associated with all of these bonds added together. In a saturated fat the acyl chains are able to align perfectly right along their length, maximising intermolecular interactions. This effect is reflected in the fact that the melting temperature of a pure triacylglycerol increases as the chain length increases.

You can see this effect clearly in the melting temperatures of individual fatty acids. (C18:0 means an 18 carbon molecule with zero double bonds in the acyl chain):

C18:0 (stearic acid) 70°C

C16:0 (palmitic acid) 63°C

C14:0 (myristic acid) 58°C

So the addition of a single -CH₂- group in the acyl chain increases melting temperature by a few degrees.

When a cis double bond is introduced into the acyl chain this creates a kink in the structure. Because of this the acyl chains cannot align completely along their length - they don't pack together as well. Because of this the sum of the energy associated with intermolecular Van der Waals interactions is reduced. Again this is seen clearly in the melting temperatures of fatty acids:

stearic acid C18:0 70°C

oleic acid C18:1 16°C

As you can see from these numbers, the effect of introducing a double bond is large compared to the chain length effect.

A typical fat or oil will of course be a mixture of different triacylglycerols, but the underlying principle is the same.

ecology - If I built a concrete pool, would it ever contain fish?

The answer is yes, absolutelyvne enough time. You can do this experiment yourself. Get a clean glass jar, hell even sterilize if if you like (your oven overnight at 250 F will do it). Fill it about 3/4 with clean (or even sterilized) water, and leave it outside in a mixed sunny shady spot for a few weeks, in moderate weather. It's small volume will get cooked by constant direct sun, which will impede the results.
After a few weeks (might be faster), look closely into the water (through the sides of the jar) with a magnifying glass, or better still, sample the water and look under a microscope. You won't see, but they are there, multiple bacterial species.
You will see single celled algae, small pond creatures (hydra, rotary-topped species (multiple)), paramecia, and multi-celled algal forms in strings. These are all fallen in from airborne dust and windblown particles. You likely won't get fish, but if you are lucky, you might get a few brine shrimp. And yes, particles of blown or bird-carried dirt etc can easily carry shrimp, amphibian, or plausibly, viable fish eggs.

But what do they feed on? There's no food in the water you put in !! CO2, nitrogen, Oxygen, etc are readily available from the air. A few cells of bacteria or algal forms seed the clean water, and begin fixing CO2, nitrogen etc, and now you have a food source. Wind-carried (or bird-carried) small organisms can now survive in a web of bacteria-plant-animal interactions.
By the way, you can also run a control jar, where you sterilize the jar, fill it with boiling hot water, and quickly cover it tightly with foil. Place it beside your open jar, and it will grow...nothing.

As a side note, "toxic" algae are often not toxic to small organisms and other algae. Their toxins (neurotoxins usually) affect mostly only higher organisms, such as fish and humans. Algal blooms kill fish and birds, they seldom sterilize the pond.

gene expression - Do the phage repressors CI and Mnt exhibit crosstalk?

There are no reports for it yet. I don't think just because they show overall homology, they would exhibit crosstalk. Just see the alignment of the DNA binding domains of these proteins first ~70 residues from N-terminal. Moreover their DBDs belong to different PFAM families.

Similarly with the promoter sequences.
As reported in iGEM website:

They are quite different.
Moreover, if iGEM has a reported standard part such as a bistable system component: Mnt/cI promoter (BBa_K228003) then it would have been pretty much standardized. iGEM parts are usually reliable.

bioinformatics - Superposing DNA - Biology

Try this out with BioPython:

from Bio.PDB.PDBSuperimposer import PDBSuperimposer as superimposer
from Bio.PDB.PDBParser import PDBParser

parser = PDBParser()
sup = superimposer()
struct_1 = parser.get_structure("XXXX","first_pdb")
struct_2 = parser.get_structure("XXXX","second_pdb")

atoms1 = struct_1.get_atoms()
atoms2 = struct_2.get_atoms()
sup.set_atoms(atoms1,atoms2)

print sup.rotrans #print the rotation translation matrix from the SVD

#then to complete the alignment
sup.apply()  

You can look here for further details. SuperPoser

entomology - Do insects respond to the detection of dead insects?

Yes, it is a common behaviour and is called necromone signaling (Yao et al 2009, see references in paper for many examples), and is probably used to avoid predators, parasites and disease. The chemicals used are often similar (unsaturated fatty acids), and seem to have an old evolutionary history (~400 million years). Many groups of species can also detect infected, not yet dead, conspecifics. Removal of dead individual is also common in e.g. ants (necrophoric behavior).

The paper referred to earlier (beside reviewing earlier evidence) also provides experiments of detection/avoidence in isopods and Tent
caterpillars (Malacosoma americanum), where they show avoidance based on crushed conspecifics, unsaturated fatty acids and (for isopods) intact corpses.

Naturally, the same type of compounds are used by e.g. species of carrion beetles (Silphidae) to find their animal hosts, but then for the purpose of reproduction.