I recommend Platinum crucible. They are usually inert and easy to clean. They are more expensive than aluminium crucibles, but last much longer. It depends of course also on your budget which crucible you use. I have added an overview of Mettler-Toldedo.
It depends on the maximum temperature required by you in the thermogravimetric analysis. Usually, aluminum pans (crucibles) are used up to 600°C, while platinum and alumina pans are used up to 1.000°C and 1.500°C, respectively. However, you have many types of pans, like gold and quartz pans. You can choose any types of pans for oxidative or reactive atmospheres, since your raw material is slow pyrolysis bio-oil. I recommend you use open pans, since you need to take into account all reactions like volatilization of any substances. Sealed pans are most appropriated for DSC analysis (to observe heat flow changes) because sealing the samples you avoid events like loss of volatile compounds and moisture. However, it depends on the desired application.
Hey buddy, it depends. In general a Pt crucible is much more inert than its alumina conterpart under high temperature. However, alumina is much more cheap. In your case, I guess pyrolysis of bio-oil happens under 1000 degree celcius, where alumina crucible would be enough to satisfy your needs. Thus, I recommend alumina crucible.