Hydrogen bonds can be formed between the -OH groups of MWCNTs and groups of your polymer. Depends of course what polymer you are using as matrix. FTIR spectra can confirm hydrogen bonding, you will observe shifting of the relevant peaks.
it depends on polymer, in particular its homo/lumo energy levels; transient absorption spectroscopy should be useful for that ; or fluorescence quenching could be sign of CT
With respect to "pristine" MWCNT without any covalently bonded functionality, consider that each carbon has a 2pz atomic orbital containing one electron, and the surface population of such orbitals defines an extremely delocalized pi system. This system exhibits very strong pi-bonding overlap with polymeric groups that have pi-bonds themselves. Many surfactants and polymers having such delocalized pi systems in functional groups have been found to bond strongly to MWCNT (as well as to other graphenic surfaces). Short pi systems (delocalized over 1-4 atoms) do not interact as strongly as delocalized ring and multi-ring systems. Polymers with imidazolium groups are perhaps the most strongly binding polymers to MWCNT (see attached file). It is arguable whether one can call such pi-pi overlap "charge transfer," as the phrase "charge sharing" is probably more appropriate.