thor - I'm not familiar with this particular churchyard, but am with others that go back beyond this date. As regards the lack of headstones I see silvery has already mentioned that the family may not have been able to afford the cost - another factor may have been that they weren't literate at this stage & taken the view that they knew where the grave was, so why put up a marker that they couldn't read? Otherwise, has this churchyard been tied/cleared at some stage & headstones removed - eg to round the walls or as paths - it does happen.
I think silvery's question
Is there any register of where people were buried?
is asking whether there is a map/plan that shows grave plots & names.
if there was any order in which people were buried?
I think in early times people were buried around the church, gradually spreading out; then at some point a section might be started & all the graves in that area used before a new section was created. If there are enough stones it may be possible to tell by looking at the earliest burial listed on each. On the other hand I've seen graves tucked into odd corners etc "out of order" presumably either because someone had reserved a particular plot or because the existing space was virtually full & new land not yet available.