How does branching affect the melting point of a polymer?

In almost all ordinary cases, adding a small amount of solid impurity to a solid compound will cause a decrease in the melting point of the resulting mixture. The explanation can be complicated if one wishes to examine the physical chemistry equations involved. One can simplify the explanation by the following process. The solid phase of a pure chemical is characterised by having all the molecules fitting into a crystal lattice, where the molecules are oriented in a symmetrical, low energy and stable fashion. When one adds some “foreign” molecules (impurity) to the crystal and grinds up the resulting mixture, these foreign molecules usually weaken the original crystal structure because its molecules have a different shape and size. This makes it easier to break up the crystal by applying heat (or melting). If it is easier, then the melting occurs at a lower temperature than for the pure substance. There are rare exceptions, however. When two different solid compounds, called enantiomers,, are mixed together in a certain proportion, the resulting melting point can be higher than that of the pure enantiomer’s melting point. This is due to the formation of a “racemic compound”. In this case, adding the two chemicals together actually stabilises the crystal structure of the resulting mixture. If you are curious about this you can research this topic in the literature or the web.

polymers is that they will not melt when heated. ... softening polymers have weak intermolecular forces holding the chains to each other. thermosetting polymers do not melt when heated and that's because they have strong cross links holding. the chains to each other.

A low density results from the chains being further apart. Lower melting points and tensile strengths are evident, because the intermolecular bonds are weaker and require less energy to break. Branching makes the polymers less dense and results in low tensile strength and melting points. The polymer melting point Tm is increased if the double bonds, aromatic groups, bulky or large side groups are present in the polymer chain, because they restrict the flexibility of the chain. The branching of chains causes the reduction of melting point, as defects are produced because of the branching.

Almost nothing.

I guess you are referring to a simple melting point equipment e.g. a microscope with a heating plate (or -oh horror- a Thiele tube)

That type of equipments are used to measure the melting point of low molecular substances.

In polymer chemistry the melting point is often not as sharp as with low molecular substances. A simple visual inspection will not help you much; so as a polymer chemist in order to study melting and crystallization you need e.g. a DSC. or even better a modulated DSC (see MDSC)

The boiling point is a temperature where a compound has enough energy (usually heat) to overcome the surrounding atmospheric pressure and “escape” into the gas phase.

If the pressure increases then it is harder to reach this point, the boiling point temperature will increase.

If the pressure is lower then the boiling point will be lower. If you lower the pressure enough, by creating a partial vacuum, you can make fluids boil at much lower temperatures. It is possible to get water to boil at room temperature with a very low pressure.

Branching affects chain entanglement, the ability of chains to slide past one another, in turn affecting the bulk physical properties. Long chain branches may increase polymer strength, toughness, and the glass transition temperature (Tg) due to an increase in the number of entanglements per chain.