Hi Jaeun,
You can align and transform them more or less to a general head model, though never perfect. But that would be useful when you want to compare results for many different individuals. In that case you map the results from the individual case via that transformations again to the general head model.
The leadfield however still would have to be on the original head model, because the brain topology, cortical orientation, skull thickness, possible pathologies etc. have a big influence on the leadfield matrix.
I do not fully understand this part of the question, though using the same cap for different people will get different locations of the electrodes on the scalp, thus different lead fields.
You can use the same standard head model for everyone with standard position electrodes, though that will give quite an approximation error depending on what you want to do with your data.
Kind regards,
Steven
Ps: A nice paper on the effects of errors in forward modelling is the following:
Akalin Acar, Z., Makeig, S., 2013. Effects of forward model errors on EEG source localization. Brain Topogr. 26, 378–396. Effects of Forward Model Errors on EEG Source Localization | Brain Topography