How to describe the relationship with writer of recommendation letter?
Both don't seem like unusual "relationships" at all, so I don't think there should be any issue describing them just like you did here.

If there is a drop-down list, you can select whatever is the most appropriate (presumably there are options amounting to "colleague at my current department" and "collaborator" - I think it counts as "collaborating" if you have visited them occasionally, even if you happened to not have published a paper yet). If there is a freetext field, you can just write what you wrote here.