Still feeling difficulty breathing sometimes after pneumonia. Is that normal or not?

Needs evaluation. Persistent shortness of breath needs a specific medical evaluation. For some people after pneumonia they can feel short of breath for some time, if they have a prior lung disorder ( (copd etc) on the other hand persistent shortness of breath can indicate many potential serious problems, from an incorrect original diagnosis, to a persistent infection, etc etc. Thus it needs an evaluation by an md.
Possibly. Are you getting followup? There is an old adage in medicine that the most important chest x-ray in treating pneumonia is the one taken 6 weeks after treatment (to be sure it's back to normal). If you're still short of breath, be sure to continue in the care of your doc!