When a noun describes a second noun, the second noun has an -i suffix added. But what happens when that second noun is used to describe yet another noun? Do all the nouns except the first take an -(s)i suffix?

For example:
buzdolabı rafı - 'fridge shelf
buzdolabı kapısı - 'fridge door
buzdolabı kapısı rafı - 'fridge door shelf???

Is that right?

Yes, it is correct. Here are other examples:

deniz suyu sıcaklığı : sea water heat
otobüs bileti fiyatları : bus ticket prices
hava yolu taşımacılığı : air way transport
kapı zili sesi : door bell noise

Again if we are talking about a particular object then we make it defined by adding a genitive suffix:

deniz suyunun sıcaklığı : the heat of the sea water
otobüs biletinin fiyatı : the price of the bus ticket