1. When we say we have strong emotions for someone, do we mean that we like them very much?
2. Are there any differences between 'have feeling for someone' and 'have emotions for someone'? Can you please give me some example sentences?
3. Is the sentence 'we are trying to get a feel for what he is like' saying that we are trying to understand what he is like?
2. I think that you are more likely to say that you 'have feelings for someone' in conversation. The second one doesn't sound very natural.
I think you would report that someone felt strong emotions in story writing.