Fact: Edo Tensei revives the person the exact same way they died. Meaning with all their battlegear on, age and memories from the event. The only reason Madara was revived in his prime is because Kabuto did extensive research on Madara's and Hashirama's bodies and experimented. We have that as a clear statement when Madara is revived.
As to how Hashirama could have died, I can say one thing - nobody is immortal and nobody is invincible. That is proven with the death of the Third Raikage. Not: the man took on the 8-tails solo. He is said to have died fighting off an entire enemy army ( I think roughly 20000 enemy shinobi) and after 3 days of non-stop combat, he died.
A possible time-line could be the following:
The Hidden Leaf is created. -> Madara deserts the Hidden Leaf. -> Hashirama attends the first 5-Kage Summit and distributes the tailed beasts among the villages. -> Madara fights Hashirama and is defeated (also killed). -> Hashirama obtains the 9-Tailed beast. -> Marries Mito Uzumaki (who also becomes the first jinchuriki for the 9-tails). -> Has a child (the gender is unknown). -> Randomly fights le' wild Kakuzu. -> Trains Hiruzen. -> Some 18-ish years pass (in order for his child to become of age for marriage) and his child gets married. -> Has a granddaughter named Tsunade. -> Some 5-6 years later he dies in one of the many wars. -> Tobirama becomes Hokage.
Here is where it gets interesting. The exact age of Hashirama is a mystery. He could be 30 years old when he does, or 40 but not older than 50. Let's assume he is 20 years when he founds the Hidden Leaf. He then kills Madara and obtains the Kyuubi. Let's say this all happened in a span of 2-3 years. After Madara's 'death', Hashirama is 23. He marries Mito and has a child. He is now roughly 24. After some 18 years his child marries (best case scenario) and has a child of his own - namely Tsunade. Hashirama is 42-43. Another 5 years pass for Tsunade to grow and he is now roughly 47 years old. He then dies in a battle. However..
It is shown that after his death Tobirama becomes Hokage. As his brother, he should be roughly the same age as Hashirama - best case scenario 2-3 years younger. So later on Tobirama sacrifices himself so his team can escape. In his team we note Danzo Shimura and Hiruzen Sarutobi. Hiruzen becomes Hokage. Some time afterwards we can see Orochimaru, Jiraiya and Tsunade taking the all-too-familiar bell test. Let's assume Tsunade is roughly the same age as when Naruto and co. took the test - 13 or 14. Best case scenario 8 years have passed since Hashirama died. Which would bring Tobirama to be somewhere near his fifties at the time of his demise (considering Hiruzen had 2-3 years as Kage before taking up the Sannin. Which, in my opinion, is kind of confusing, since they both look quite young when resurrected.
One possible solution to this would be that Tobirama became Hokage way before Hashirama died. This would mean that they bouth could have died in the same time period or even the same war. Let's say After the birth of his Granddaughter, Hashirama gives the title of Hokage to Tobirama. This means that in 5 years time he would meet his demise, and soon afterwards Tobirama would follow.
This is the best I could come up with. If anyone else has any ideas, share.