If any kind of halv-dwarves would exist it would probably be a union between a dwarf and a man of some sort.
Probably some form of man that resemble dwarves a bit, some form of short, mountain-dwelling bearded people. If a group of men would ally themselves to the dwarfes somewhere and basicly live with them in mountanious areas and then more and more resemble them in clothing and style (beards) and share their love for craftmanship and gems, this might be possible.
But I'm a bit unsure if the dwarf part would be the man or the woman, dwarves might find female humans more fysicly attractive then their dwarven ones, but on the other hand they like beards which female humans doesn't have, so if a nice male human came along some dwarven woman and let's say that he was skilled in craftmanship, un-.humanly strong (since dwarves are stronger than men), and with a mighty fine beard perhaps some magic could happen. But the lack of beards would probably be a problem for male dwarves and the lack of strength a problem for female dwarves. The uglyness of dwarves (especially female ones) would be a problem for humans.
Concerning hobbits and dwarves this is maybe even more unlikely than other humans. Hobbits live simple lives and don't enjoy hard labour that much as dwarves do, and interbreed with hobbits would be even worse for dwarves than with men since they would become smaller than dwarves and weaker than a dwarf-normal human mix.
Buuuut on the other hand some of the 3 races of hobbits have some resemblence to dwarves
Stoors: "They were broader in build than the other Hobbits, and had large hands and feet. Among the Hobbits, the Stoors most resembled Men."
Harfoots:T"he Harfoots liked highlands and hillsides, and were accustomed to living underground longer. They were also on very friendly terms with the Dwarves, who travelled through the High Pass on the Great Road."
Harfoots seems quite a match but then: "They were shorter and smaller than the other breeds, browner of skin, HAD NO BEARDS, and did not wear any footwear. They lived in holes they called smials, a habit which they long preserved."
Stoors are bigger than other hobbits, and resemble men more and probably also had beards, the physical appearance of stoors are closer to that of a dwarf.
Harfoots were apperently friends of dwarves and lived in holes under the ground but were shorter than other hobbits (and dwarves of course) and had no beards, and that is a mayor issue.
And then it is worth to mention that dwarves aren't very socialb ewith other races, they never learn other peoples their language, Khuzdul and doesn't even use it or their actual names when non-dwarves are present. There is just no way a dwarven society would accept a union between a dwarf and a non-dwarf.
"To answer some questions: How would Durin's folk regard half-dwarven folk?"
They would not accept interbreeding between dwarves and other races but would probably be sort of friendly to halv-dwarvs if such a folk would be discovered, if we say that the Umli existed they would probably be seen as a sort of kin by dwarves but not equal to dwarves themselves, and intermarriage could happen, but i do think that such an intermarriage wouldn't be accepted that much either since it would also mix out their blood, if not as much as if it happened with a full human. I picture Durin's folk as more proud than other dwarves so they would probably be the least accepting of such things and the last to mix with anything non-dwarfish. So intermarriage with non-dwarves would not be accepted but if a people that were halv-dwarven were discovered dwarves would probably regard them as kin even if they would have wish that sucha union never happened in the first place.
"How would Thorin Oakenshield regard them? Or say any other member of his company?"
He would dislike such things a lot, proud dwarf as he is he would see such race mixing as treason agains tthe dwarves. If a people such as the Umli would be discovered he would probably be the last to referr to them as "kin" and dislike their entire existence. But as all other dwarves he would enjoy their company more than the company of other non-dwarves.
"Would the dwarves accept half-dwarves into their society?"
Some societies maybe, but i think that they would be more like allies and that intermarriage between the to would be sparse if not completely avoided. Seeing half-dwarves and dwarves living together would only happen out of emergency, like war and such things, and intermarriage would be the result of close contact. But no doubt there would be great friendship between the half-dwarves and the dwarves.
"Would half-dwarven women be more accepted than men?"
No, beacuse less beards probably. But idk they would probably both the accepted in the same way.
As a last commentary i would say that the grade of acceptance would vary with how dwarvish the halv-dwarves are, If they live like men with men they would probably be considered as not much more than men, but if they themselves lived under ground and mined and lived dwarvish they would be seen as more like dwarves and kin.
And dwarf-elven? No. Dwarf-orc? Only through eventual rape bu seen how strong dwarves are and how it's hard to see the difference between a male and a female dwarf this is ot likely either. Dwarves would not accept an individual that is half-orc.