hashirama cudnt go to the pure world, he was ressurected back by orochimaru and so did tobirama. We've had tips/hints on how tobirama could have died. But how Hashirama died is still the biggest question about him. The manga is bragging about him so much and stuff but still no sign of a clue about how he died. Basicly, he cant have died by natural death, or else his time would have been up and would go to the pure world. Simply put, he either died duo injuries or has been killed.( but assuming from latest mangas on how madara talked about him, he could never have died from injuries and could never have died in battle ). So we've had this already, what other option is left ? Sick / ill just like itachi ? I still doubt that. I mean a man who's supposedly have an indistructable body which is full of LIFE, cant be injured in battle or be killed can be sick ? Doesn't sounds very convincing does it ?
You're theory about tobirama wanting to get back hashirama by edo tensei is good, but the way you're explaining about hashirama doesnt compensate with the manga itself. Theory is 1 thing but facts are known and always > theories.
Also you said that madara came back with rinnegan to fight again ? Madara stated himself he activated ''these eyes'' right before he died.