Yes, Dumbledore did know that Voldemort would return:
‘Yes, sir. Well, Voldemort’s going to try other ways of coming back, isn’t he? I mean, he hasn’t gone, has he?’
‘No, Harry, he has not. He is still out there somewhere, perhaps looking for another body to share...not being truly alive, he cannot be killed¹. He left Quirrell to die; he shows just as little mercy to his followers as his enemies. Nevertheless, Harry, while you may only have delayed his return to power, it will merely take someone else who is prepared to fight what seems a losing battle next time – and if he is delayed again, and again, why, he may never return to power.’
Philosopher's Stone - page 216 - UK - chapter 17, The Man With Two Faces
Thing is, there are multiple ways of returning a spectral form of a witch or wizard to a corporeal form -- the philosopher's stone; unicorn's blood; possession of another person; the resurrection potions (of Voldemort's creation). The Horcruxes kept Voldemort's spirit alive, but did not prevent him from being greatly debilitated. Dumbledore, however, did not know about the Horcruxes until the time of the events of Chamber of Secrets
As Kevin mentioned in his comment, regarding the ghosts, Seamus Finnigan asks Nearly Headless Nick why the Baron is so bloody:
‘How did he get covered in blood?’ asked Seamus with great interest.
‘I’ve never asked,’ said Nearly Headless Nick delicately.
Philosopher's Stone - page 93 - UK - chapter 7, The Sorting Hat
So it's possible if Nearly Headless Nick didn't know about The Grey Lady and the Bloody Baron, then the other ghosts didn't either. The Grey Lady had a big motivating factor to not tell anyone her story: personal shame over the theft of the diadem from her mother, Rowena Ravenclaw. Canon doesn't specify.
I will say it does seem hard to believe that Dumbledore himself didn't know the story; however, if he had known, I think he would have immediately questioned the Grey Lady and would have undoubtedly found out about the diadem (because he's Dumbledore!) We have to consider the possibility that he hadn't gotten that far in his search for clues and Horcruxes.
Dumbledore did not know about the Horcruxes at the time of James and Lily's death or during the next eleven years. It wasn't until after he viewed Slughorn's memory with the Horcrux conversation between Slughorn and Tom Riddle during Harry's 6th year that Dumbledore knew unequivocally that there were multiple Horcruxes, although he suspected that possibility after the events in the Chamber of Secrets:
‘The careless way in which Voldemort regarded this Horcrux seemed most ominous to me. It suggested that he must have made – or been planning to make – more Horcruxes, so that the loss of his first would not be so detrimental. I did not wish to believe it, but nothing else seemed to make sense.' (Dumbledore)
Half-Blood Prince - page 468-469 - UK - chapter 23, Horcruxes
¹ Here is where Dumbledore articulates that he knows Voldemort has not fully died and, more importantly, cannot die. I think this is the first seed that is planted that will ultimately morph into Dumbledore's understanding that Horcruxes are involved.