[Cheese_Burgers]

Is it true that theoretically, a polymer's Tg does not increase with increasing MW of the polymer, as long as the monomer ratio in the chain is the same and in the same order?

[pgk]

Roughly: Solids (whether crystalline or amorphous) are materials that have all molecules in order. The melting point is the temperature (or temperature range) that the crystal lattice or any other molecular order is destroyed and therefore, melting point depends on the molecular mass because the whole molecule participates in the crystal or any other solid formation.
Although not in order in the liquid state, the polymer chains (and some long molecules) still keep their original structure in space, together with some intermolecular interactions. 
Roughly: Glass transition temperature (Tg) is the temperature (or temperature range) that some long molecules (e.g. gums, waxes) and polymer chains lose their original structure in space but most intermolecular interactions are still kept.
Question 1: Is melting point higher than Tg or vis-versa?
Question 2: According your opinion, does the original structure in space depend on the monomer structure only, or not?
Hint: Imagine the polymer’s solid state as tertiary structure and their original structure in space as secondary one (in a similar way as peptides and proteins).