1) If you cast a Tangleroot on a flying creature and then reveal it you lose the tangleroot because it is not a valid target.
2) If you cast a Tangleroot on a non-flying creature without revealing it and then the creature subsequently gains flying, then if you reveal Tangleroot, the creature becomes an illegal target and you lose Tangleroot.
3) If you cast and reveal Tangleroot on a non-flying creature and the creature subsequently gains flying, the Tangleroot remains on the creature even though it is flying.
3a) If the tangleroot gets transfused off of the flying creature it cannot then be reattached to the creature that has gained flying.
Enchantments only check their target for legality when they are attached to the creature. If I put a Bear Strength on a living creature and then that creature somehow gained "Non-living" it would retain the Bear Strength. If that creature ever lost Bear Strength I could not re-enchant it because it would now be an illegal target.
The funny thing about Mage Wars is that you can put whatever enchantment you want on anything face down. You are on your honor that it's a legal target. The only time it ultimately matters is when the enchantment is revealed and attached and everyone can see the target line. If you are in error and it is not a legal target you simply lose the enchantment and all mana spent on it. I would also assume in a tournament setting that you'd get some sort of demerit for illegal targeting as it is technically cheating. However, if the game state changes such that the original enchanted object becomes an illegal target you have not cheated, but have been outplayed
Another classic example of the finnicky nature of enchantments is Demonhide Mask. With this equipment the Warlock gains the demon subtype when making an attack. If you have another demon creature that is enchanted with Demonic Link and Enchantment Transfusion you are legally able to transfer Demonic Link over to the Warlock equipped with Demonhide Mask during an attack sequence because the warlock is considered a demon creature at that point. After the attack Demonic Link is not destroyed because there isn't a constant targeting check. Targeting is only checked during the instant that the enchantment is being attached.