1. Most often properties of chitosan depends on method of production (thence, ash content, insoluble extracts, water content, degree of deacetylation, molar mass etc.).  Unless you use chitosan, synthesized from the same batch, you cannot have reproducible molecular characteristic data (hope this is the reason for your TGA expt).

2. You can have the meaningful molar mass data from GPC for low molecular weight or oligomeric chitosan. However, the commercial ones are most often high molar mass products, GPC will not give you meaningful answer (because of its broad molar mass distribution you will not have meaningful weight average molar mass). 

3. You can buy chitosan and its derivatives from HMC+ (you can select degree of deaceylation and viscosity average molar mass of your choice and also grade). According to your usage you can buy either pharmaceutical (biomedical allpications: insitu experiments) or practical grade chitosan. (https://www.gmp-chitosan.com/en/chitin-chitosan-shop.html).

https://www.gmp-chitosan.com/en/chitin-chitosan-shop.html

You can  Mwt of chitosan determined by viscosity method by and use Mark Houwink equation . The method is very easy and accurate   

Thank you :)