Can sheep farmer perform multiple exchanges at once?
The card doesn't say you can do multiple conversions at the same time, so they have to be sequential.

However, in other situations, it's established that you don't have to have room for animals if you're going to immediately use them for something else. For instance, if you receive animals from an action space, you can immediately afterwards cook them, without having to find room for them in between.

I would argue that the Sheep Farmer works the same way. In this case, you can use it twice in succession, without having to take animal storage limits in account.

I'll add a ruling to this effect to the next edition of the Unofficial Agricola Compendium, which many players consider to be almost authoritative.