Does kama have a place in the life of a practitioner after losing kamacchanda?

Since kamacchanda is one of the five hindrances, it seems to be something to overcome.

Yes, it is. Such as nivaraṇapabba (hindrances title) in mahāsatipatthānasutta.

Does that mean then that there is no more place for art and beauty in the life of a practitioner after the first jhana, according to Buddhist teaching?

Yes, it is till that practitioner still can keep his jhāna. But it is still can return when he loose his jhāna. Because jhāna-mind just arise instead of hindrance-mind, jhāna-mind does not destroyed chance to arising of future hindrance. It is a duty of vipassana. However, jhāna is required, for vipassanā of taṇhācarita-puggala.

Or can you have a healthy relationship with kama?

Yes, the practitioner can practice the right mettā, without kāmacchanda. But the practitioner must be smart to choose his friends (be able to all ariya)/partners (be able just for sotāpanna and sakadāgāmī), too.

Is taking pleasure in a tree or a conversation with a friend kamacchanda?

It is up to the practitioner's present, arising, mind factors on that time. See my answer about chanda here to understand about chanda.