Aaaah my dear; welcome to the world of pottery and the Mighty Deity of the Kiln God who has been observed revered in China since ancient times!
I'm afraid that with pottery you are always working with the knowledge that you can and will loose some of your work due to a lot of different factors during firing. I am a self taught potter so am no expert but here are just a few that I have contended with and still do to this day:
Different thickness of the clay. Even to this day I sometimes can find this difficult to judge especially when throwing larger pieces like the jar. Down where the transitioning between the foot and the wall of the jar is happening it is very thick which on this one I got away with it but on another has caused large stress cracks during the final fire. If it had been any thicker it would have totally exploded away and maybe even damaged other things next to it in the kiln.
Practice makes perfect!
The clay not having been dried slowly and equally enough. When your finished piece is ready to dry it is so important that it dries slowly so that the outer and thinner parts do not dry too fast and shrink too rapidly before the 'inside' has a chance to keep up. Sometimes the cracks caused by this can be minuscule and are only apparent after firing.
Opening the kiln too soon. So bloody tempting!! But let the kiln cool slowly.
I had a lot of frustrations back when others fired my work and I feel your pain. If you get the chance - surreptitiously sweep both sides of their kiln shelves. A lots of dust and grit can accumulate on them and will fall into your pots when they stack the kiln. I had one person who regularly filled the kiln with dirty hands so ended up with dirty thumb prints on a lot of my stuff that was rather sad....
For the rough bits on the undersides of your pots - use a dremmel or a sanding stone. Since with low fire you have to glaze the underside everything has to stand on little pointy stilts otherwise it would melt into the shelf.
When you glaze your work make sure that your glaze is thoroughly whisked. Use a drill with a stirry thingie attachment if you are dipping and then once it is dry I would smooth over any lump and bumps with either your finger or something else suitable.
I used to have that exact problem with my glaze being gritty and I thought firing would sort it and melt it out but it didn't.
Right, so at the end of yet another essay I would just like to say - stick with it! It is a wonderful hobby that has its frustrations; but is so worth it! And as you can see from my ramblings - it is wonderfully obsessive!
Oh and thank you for liking my jar - if you look at it funny and for too long you realise that actually the pretty flowers look like vaginas. So that's nice.