Usage of TFA in Pfitzner-Moffat oxidation and Collins vs Jones oxidation Is the addition of TFA in Pfitzner-Moffat oxidation to protonate the DCC to form a positive carbocation for the alcohol to attack? Or is there more to it? Why is TFA used and not other acids? Are other acids to weak for this?

Lastly for the Collins vs Jones oxidation, the only discernible differences are the solvent: $\ce{H2SO4}$ vs DCM, and that the Collins oxidation makes use of a pyridin chlorochromate, does this complex dampen the oxidative effect of chromium? So much so that the Collins oxidation can not directly oxidise a alcohol to a carboxylic acid, whereas Jones reagent with $\ce{H2SO4}$ and $\ce{CrO3}$ can?
Moffat &amp; Pfitzner have accidentally found their famous oxidation while working on mono-nucleotides (acually 5'-phosphates). Breifly, when pyromidium thymidine-5'-O-phosphate was reacted with dicyclohexylcaebodiimide  in anhydrous DMSO at room temperature resulted a violent reaction to give 90% of 5'-aldehyde product (Ref.1). They further pursued this finding and published their finding as specific reaction (Ref.2). The acid they have used in first finding was anhydrous orthophosphoric acid, which have given 90% yield. Hence, it is not necessary to have TFA as the acid. Following is the suggested mechanism for Pfitzner-Moffat oxidation: 



About Collins vs Jones oxidation, both of them used chromium-based oxidants. Oxidations with chromium oxidants proceed through a similar mechanism. Different between Collins and Jones are conditions: Anhydrous (in pyridine/$\ce{CH2Cl2}$) vs aqueous (use of $\ce{CH2Cl2}$). Following is the suggested mechanism for chromium-based oxidants:



After first oxidation to aldehyde, chromium oxidant needs $\ce{CH-OH}$ part available to further oxidize to carboxylic acid (see in both mechanism, how oxidation initiated and finished). In anhydrous conditions, this feature is lacked. So, oxidation stops at aldehyde moiety. However, trace of water make aldehyde in equlibrium with its gem-diol moiety, which gives the necessary requirement of $\ce{CH-OH}$ feature. So, in Jones oxidation condition, oxidation will further continue to give carboxylic acids.

References:


K. E. Pfitzner, J. G. Moffatt, “The Synthesis of Nucleoside-5' Aldehydes,” J. Am. Chem. Soc. 1963, 85(19), 3027-3027 (https://doi.org/10.1021/ja00902a035).
K. E. Pfitzner, J. G. Moffatt, “A New and Selective Oxidation of Alcohols,” J. Am. Chem. Soc. 1963, 85(19), 3027-3028 (https://doi.org/10.1021/ja00902a036).