Stone mortars and pestles have been used by the Epi-Paleolithic (Mesolithic) Kebaran culture (the Levant with Sinai) from 22000 to 18000 BC to crush grains and other plant material. The Kebaran mortars that have been found are sculpted, slightly conical bowls of porous stone.link
Were there any stone vessels (including mortars) made in Paleolithic?
The period in the near east right after the Epipaleolithic in that same area is often called the Pre-pottery Neolithic. This name is of course because it contains pretty much every kind of artifact one would expect of the Neolithic, except pottery. That hadn't been invented yet (in this area). This is when we find all kinds of stone (not pottery) bowls. So they made and used stone vessels, but hadn't worked out (or borrowed the tech for) pottery yet.
For the Epipaleolithic I don't know that we've got anything found that served only as a bowl. There were of course some mortars found, which are essentially small sturdy bowls specially made for grinding down grains. Pot shards are very common finds, once pots came into existence, so most likely if we haven't found those they largely didn't have them. The main innovation of this place and time was learning to use wild grains to make flour. Bread of course can just be baked on a big flat stone, so no special new fire-proof container was really needed.
Yes.
I should qualify this at the start, evidence of deliberate working to produce a bowl shape is very hard to come by and bowl shapes are produced naturally during extensive grinding - so if you have a stationary rock with a slight depression that holds your grain or ochre well, you might work in this area with a pestle (or equivalent device) and over time produce a deeper bowl. This isn't deliberate working, just a nice incidental feature.
There is evidence of bowl shapes being produced by grinding back to as far as the Acheulean (1.95–0.13 Mya) at the 8-B-11 site at Sai Island in northern Sudan as determined by Van Peer et al, 20031.
Their extraordinary find is a large piece of sandstone rock that shows working in several contexts, from flaking to grinding, you can see the ground bowl-shape in the middle-lower left, above the brackets with a label saying "ancient fracture":
Image attribution: From reference 1; Copyright © 2003 Elsevier Ltd.
According to the article, there is some evidence of this depression being cut out and shaped deliberately, and several pieces of non-native stone (chert) with residues of ochre were found in the vicinity, so this depression may have been used to grind ochre.
More recently, Hayes2, in a 2015 unpublished thesis found evidence of grindstones/millstones with bowl-like depressions in Australian First Nations cultures dating back to about 45 Kya. This date would put it in the range of the upper paleolithic, though how these dates apply to stone-age cultures outside of the Western Europe/Middle East I don't know.
Refs:
Van Peer P, Fullagar R, Stokes S, Bailey RM, Moeyersons J, Steenhoudt F, Geerts A, Vanderbeken T, De Dapper M, Geus F. The Early to Middle Stone Age transition and the emergence of modern human behaviour at site 8-B-11, Sai Island, Sudan. J Hum Evol. 2003 Aug;45(2):187-93. doi: 10.1016/s0047-2484(03)00103-9. PMID: 14529653.
Hayes, E. 2015 What Was Ground? A Functional Analysis of Grinding Stones from Madjedbebe and Lake Mungo, Australia. Unpublished PhD thesis, Centre for Archaeological Science, School of Earth and Environmental Sciences, University of Wollongong, Wollongong
