If a person has gallstones that don't dissolve with medication, can the gallstones be surgically removed without removing the gall bladder?

No. The problem with gallstones is the gallbladder. Stones indicate that the gallbladder is diseased and needs to be removed. It is not the standard of care to just remove gall stones.
No. In the old days they used to use laser therapy to break up the gallstones similar to kidney stone treatment. However it was soon discovered that as long as the gallbladder was there to produce the stones, removing just the stones was useless. Since the gallbladder is not an essential organ, definitive treatment for gallstone disease is gallbladder removal.
Never done. Theoretically, we can open the gallbladder, remove the stones, and then close the gallbladder, but this is not how gallbladder disease is treated. The reason we remove the gallbladder is because new stones will form if we don't. Prior to laparoscopic surgery, we experimented with alternative ways to remove stones such as lithotripsy and dissolving agents; they all failed when the stones returned.
No. While it is technically possible to remove a gallstone and leave the gallbladder this is not done. If someone has gallstones requiring surgery, the entire gallbladder should be removed to prevent recurrence. Fortunately, the gallbladder is not an essential organ and people return to normal after removal.
Rarely, yes. Not routinely. But in very sick patients in the icu, for example, sometimes a drainage tube is inserted though the skin//muscle into the gb to drain it to buy some time until the patient is well enough to have proper surgery. In general the answer is no, however.