The question is how could Dumbledore have known these things? Harry was the only surviving witness to what had occurred that night, so the most plausible explanation is that Dumbledore used Legilimency on the baby to discover what had transpired – a completely reasonable course of action.

The prophecy alone does not explain the risk Dumbledore took in allowing an eleven-year-old child to face an adult wizard possessed by Voldemort. If Dumbledore had believed the prophecy and therefore that Harry would need to kill Voldemort or die by his hand then surely setting up such an unequal confrontation between the two adversaries would have promoted the latter outcome – a reckless and unnecessary risk. Dumbledore didn’t believe in the literal interpretation of prophecies though10 and keeping Harry alive was not his primary concern. He was honing a weapon and if Harry should die, it would be no great tragedy as that fate awaited him anyway.

Dumbledore sent Hagrid with instructions to bring Harry to the Dursleys before he had a chance to set eyes on him.

I agree Dumbledore was honing Harry as a weapon, but he was also taking basic precautions to give him a chance at survival. That's why Dumbledore did try to return in time to when he knew there was a good chance Harry would be confronting Quirrellmort. (And why he instructed Snape to watch out for Quirrell) No point in losing a weapon before it was most useful.

I agree Dumbledore had set Snape up for death over the Elder Wand business. There were plenty of ways Dumbledore could have prevented Snape's death. I can understand why he did not do so before his own death - he may have feared Snape would want the Wand and its powers for himself (as opposed to being in custody of a retired Elder Wand - which was IMO Dumbledore's original plan). He may have feared that knowing Dumbledore's other motives in planning his death by Snape would have caused Snape to perceive the killing of Dumbledore as something other than a mercy killing, and this would have damaged Snape's soul. But after his death Dumbledore's portrait was so communicative, he could have told Snape to get the wand and destroy it already, or hide it where Voldemort won't know to look for it. But then, the wand still held its power, because Draco had defeated Dumbledore before Snape got the chance to carry out their plan. If Snape (who was wizarding raised, and therefore knew the Tale of the Three Brothers) figured out the reason Dumbledore's wand was so significant he could have figured out Draco was its Master. And he could have arranged to defeat Draco without harming him (so even the Unbreakable Vow wouldn't have kicked in), thus gaining Mastery of the Wand for himself. I think Dumbledore, from his experience with the resurrection stone, did not trust Snape to be immune to the temptation of the Elder Wand. He feared of what Snape might have done had he gained mastery of the wand and knew it. Thus Dumbledore avoided saving Snape because of the possible risk to his plan to defeat Voldemort. I do hope he regreted Snape's death at least as much as Voldemort did.

We actually don't know this. The pivotal scene in PH is ambiguous, but the fact is that when Hagrid arrives with Harry it has been 24 hours since the attack on Godric's Hollow and Hagrid cannot have been traveling all that time. While this is certainly the first time DD and Hagrid have spoken, this does not preclude DD from having seen Harry without Hagrid present. Here's what easily might have happened:

Hagrid pulls Harry from the ruins of his house and takes him to some safe location belonging to the Order of the Phoenix to have his injuries (he surely had at least a few) healed. While Harry is being tended by the other Order members, Hagrid goes off on some errands for DD. In the meantime, DD arrives to see the child. It is frankly inconceivable that he wouldn't have examined Harry given the extraordinary circumstances. DD then uses Legilimency to discover that Lily gave her life to protect Harry and leaves to go set up the wards at the Dursleys. Once everything is arranged, he sends word for Hagrid to bring Harry to Little Whinging.

Oh yes, Harry was an incredibly valuable weapon and DD wouldn't have wanted to lose him. But since DD's plan wasn't dependent on Harry surviving (rather the opposite), keeping Harry safe wasn't DD's highest priority.

Agreed Snape had moved on from just wanting to avenge Lily's death but he wanted justice for Lily and that meant killing V. The proof for me is his Vow with Narcissa. This meant he knew a showdown with V was inevitable amongst all the other reasons he had for taking the vow.

Hagrid claims he had orders to bring Harry to his maternal relatives by the time he was arguing with Sirius over his custody - which was immediately after their arrival at Godric's Hollow.

There was no need to know the details of the events to understand that Harry could be protected by living with Petunia. What Dumbledore needed in order to arrive at this conclusion was knowing that Lily was killed despite Snape's request to Voldemort, Harry survived and Voldemort was gone (this may have been verified by Snape who may have noticed changes to his Dark Mark). Voldemort promised Snape that he would spare Lily if she acted 'sensibly'. The fact that she died suggested she did not, but instead tried to interfere. Harry survived - suggesting Voldemort was somehow prevented from killing him, despite the fact that there was nobody living around to fight Voldemort. Conclusion: Harry was protected by someone no longer living.

It [Harry's life] was high enough for Dumbledore to sit by Harry's bedside until he came to...

Agreed Snape had moved on from just wanting to avenge Lily's death but he wanted justice for Lily and that meant killing V. The proof for me is his Vow with Narcissa. This meant he knew a showdown with V was inevitable amongst all the other reasons he had for taking the vow.