It's an epitaph.
A phrase written on a tombstone is referred to as an epitaph.
tombstone writing i beleive
Writing that sounds poetic, as in the lyrics to a song.
An inscription is writing carved into something. For instance the writing on a tombstone.
inscription is the word you're looking for.
"Requiescate in pace" literally translates to Rest in Peace, in the film Tombstone it was reversed to in pace requiescate for reasons of poetic measure.
psalm
The poetic form is called a sonnet.
Incomplete sentences are, in professional writing circles, such as the Oxford University Poetry Society, a poetic circle founded in 1946 by Martin Starkie which aims to be the centre of poetic life within the University of Oxford.
they are called epics
It's part of the inscription.
The cheapest tombstone that I have found is at a site called Headstones and Memorials. I added their link in the related links. Their tombstones start at $285 including shipping.