I don't understand the difference between the all vs first or last or arbitary option in the annotatePeakInBatch function.

When we select all, is that mean the peak is getting annotated for more than one genes and all those genes for the peak are returned in our result and when we select other options only one gene will be returned in our result?

Also which will be the better to use when I'm annotating genes?

There may be instances where a given peak is equidistant to multiple genomic features. In that situation, what do you want returned? Do you want all of the features or just one? If just one, do you want it to be the first one, the last one, or a random choice?

What constitutes 'better' is not something anybody can decide for you.