Heaven is a place of eternal life, endless rewards and bounties,
When was heaven designated to be the reward for those who obey Allah?
The promise of such heaven came after the incident of disobeying Allah, then repenting by Adam. As there wouldn't be a reward without a task to accomplish! revise the description of Jannah! you will see exactly that it is prepared as a reward, at time of incident there was no takleef, i.e tasks to be accomplished by Mankind to deserve that reward!
How could the Shaytan be in Heaven? is he allowed to?
He is not allowed to the Heaven we know (promised to believers), remember that he was with Angels at time Allah commanded prostration to Adam! so he was obedient and worshipped Allah already! till he was commanded to prostrate and disobeyed.
How could Shaytan lead Adam astray?
Adam did a sin, after he forgot the warning Allah had warned him before! Shaytan whispered to him, and he forgot; so approached the tree, and so, committed the sin, in other words, it was Adam who allowed whispers to mislead him.
How did Adam sin if he was a prophet? was he?
Yes he was, but the prophecy started after he descended to earth! not before, so the sin of prophet Adam happened before he was a prophet.
How may forgetting be a sin? if it's out of our hands?
Forgetting is a sin if it caused us to do what is not allowed or not to do what is required. One beautiful fact is that , a sin doesn't count a sin, till it fulfills one of the following conditions: remember/realize it, if you do it without knowledge, or if you didn't have the intention! As of that moment you are required to repent and fix things.
Many people might think that we would have been in heaven now if the incident did not take place and this is funny to think! in fact what we need to see is; Allah had decided to make Man on earth before the creation of Adam (recall what He told Angels in Sura Baqara). but the incident was to give the lesson to Adam. His fate was to be on earth, to live and worship Allah. The whole life is about freewill, and Adam failed in the first test, but Allah forgave, and accepted repentance.
What about the Original Sin concept taught in Christianity?
Adam sinned, and his sin is described as a SLIP in Quran. remember it was not intentional because he forgot.
Adam REMEMBERED that he'd done wrong, and, repented, and beautifully Allah forgave him.
So he did the sin, and he repented, and Allah is forgiving, nothing like burdening his children with they have nothing to do with it, even Quran describes it as a SLIP not Major Sin.
The topic is not a simple one, I hope I could shed some light on the different aspects of it.