What is the structure of trifluoromethanesulfonic acid in the gas phase?
Has the structure of trifluoromethanesulfonic acid or a structurally strongly related acid been studied in the gas phase? (Please provide a reference)


Yes. See Gas Phase Structure of Methyl Trifluoromethanesulfonate, CH3OSO2CF3, and Conformational Properties of Covalent Sulfonates Inorg. Chem., 1999, 38 (13), pp 3051–3055 and references cited therein, especially Electron Diffraction Investigation of the Molecular Structure of Trifluoromethanesulfonic acid (triflic acid) Z. Naturforsch. Teil A 1981, 36, 917


  Does the experiment suggest equivalent or non-equivalent oxygens?


Non-equivalent. 

The 1981 paper finds 

S=O 141.7 ( 1) pm
S-O 155.7 ( 2) pm


  How well can that idea be extended? e.g. should one consider the structure of formic acid to be C2v symmetric rather than Cs?


From the following gas phase study, I don't think that gas phase formic acid monomer is C2v.
http://actachemscand.dk/pdf/acta_vol_23_p2848-2864.pdf


  Do (solid-state) crystal structures or other experiments exist that confirm a different structure for solid TfOH?


Quoting from Trifluoromethyl Chlorosulfonate, CF3OSO2Cl: Gas Phase and Crystal
Structure, Conformation and Vibrational Analysis Studied by
Experimental and Theoretical Methods Inorg. Chem. 2003, 42, 7297-7303

"The structure of triflic acid, HOSO2CF3 (trifluoromethansulfuric acid), was also studied by GED, and an anti orientation
was assumed in the analysis of the diffraction pattern. [reference 6: the 1981 reference above] In
contrast, an X-ray investigation of 2HOSO2CF3 [dot] H2O [ie. the hemihydrate] resulted
in gauche orientation of the O-H bond,[reference 7] in accordance with
theoretical calculations. [references 8 and 9]"