Why in some episodes do Pooh and friends seem to live with Christopher Robin in his house rather than in their own houses in the Hundred Acre Wood? Because they're Christopher Robin's stuffed animals. They really do "live" in his house: the Hundred Acre Wood is just where he imagines most (but not all) of their adventures taking place. This also explains some of the Bizarro Episodes, like "The Piglet Who Would Be King" or "Cleanliness is Next to Impossible." The entire series arguably takes place in Christopher Robin's imagination as he plays with his toys, so naturally some crazy things sometimes happen.
Whenever the characters do something wrong, such as in "Balloonatics" and "The Wishing Bear", they attempt to either make amends themselves or cover it up for fear of Christopher Robin turning on them. It’s reminiscent of young children who have committed a minor misdemeanour and worry about the consequences that may come of it. Being Christopher Robin's stuffed animals, he projects his feelings onto them. Case in point, in "Home is Where the Home Is", after breaking a family heirloom, Christopher Robin decides to run away.
Tigger attempting to be a rabbit and a bear in "Stripes" subtly foreshadows Eeyore's message that he will always be Tigger, with or without his stripes. He takes pity on a hungry bug and feeds it a tomato. The bug brings friends who eat everything Rabbit has grown. Tigger ruined Rabbit’s garden, which he always does with his bouncing. When Pooh tries to teach him to be a bear, Tigger ends up being attacked by the bees. Tiggers don’t like honey.
In "Friend, In Deed", Rabbit gets honey for Pooh after realising that Pooh tried to give him a jar of honey to stop him "moving away". How was he able to get it? The honey tree was unguarded because the bees drowned. They were still stuck in the door after Gopher flooded the tunnel.
This explains why Rabbit was eager to help Tigger drag Piglet onto a quest to find the Land of Milk and Honey in "The Piglet Who Would be King"; he wants to make up for unintentionally causing this to happen.
In "Find Her, Keep Her", whatever happened to Kessie's parents? Were they killed in the blizzard that Rabbit saves Kessie from at the beginning?
Perhaps. Another possibility is that they lost her while flying south for the winter.
In "The Piglet Who Would Be King," Tigger mentions his mother and comes close to tears as he talks about her. Other episodes clearly state that Tigger is the only one of his kind. The obvious implication is that his mother is dead, as are any other tiggers who might have lived before him.
