First thing is to try… You probably want rather aggressive augmentation and maybe see if you can get more unlabeled data.
Regarding transfer learning: You could try to duplicate and scale down the three channel weights in the first layer or add just a little noise, but one of the key observations is that transfer learning works best when the pretraining inputs are related to the final purpose (e.g. imagenet pretraining and then using it for medical imaging is not as useful as pretraining on medical imaging to start with).
Regarding the input sizes: So performance will degrade if you dramatically change the resolution but you can get by with changing the size.