Ok, we have the by the book, what Mearls has said, and how you probably want to play this in your game.
By the book, draw or stow can be done for free, you can do one of these per turn as the part of a move or action. However, if you want to do both, you're stuck burning your action to do so. If you're TWF you're in an even worse way, (though the Dual Wielder feat fixes the action economy here).
PHB page p190 states:
You can also interact with one object or feature of the environment for free, during either your move or your action.
Mearls has said in tweets that you're OK to use your free action to swap weapons rather than spend your action to draw and stow. That the intent here was to curb over use and also to not burn you on the action economy to swap weapons. (see this convo)
Ultimately, for your game, I think it's up to you to decide between these two rulings. Personally, I prefer my character to not get burned by the action economy here and have ruled that quick swaps of weapons (especially when it's commonly used load outs) can be done as part of the attack. I don't make a stink about it, and assume the PCs in my games are competent at what they do.
If you really have to make this work, dropping your weapon is completely action-less, so you could do that. It's messy, and prone to issues if you get moved off your space (you can't pick your weapon back up), but maybe that's just the cost of weapon juggling?
Best Answer
Hand of the Apprentice is pretty specific. It doesn't make any allowances for weapons that are long or suspended from a chain, it's one ranged attack with a melee weapon against a target within 30 feet, treated as a thrown attack but aimed with Intelligence.
The answer to both your sub-questions is no, unfortunately. Unless you're using a weapon I'm not familiar with that has a quality that actually says "When this weapon is thrown through a creature's square in order to hit a creature behind, this weapon also has a chance to hit the creature whose square it was thrown through, as if X..." then throwing a weapon through someone's square just gives the end target soft cover against the attack, it doesn't give extra attacks.
Also, I hate to be a complete downer, but note that instant weapon doesn't combine well with Hand of the Apprentice. Instant weapon specifies "If the weapon leaves your hand at any time, the spell ends at the beginning of your next turn." It's missing the all-important clause "...unless the weapon has returned to your hand." so if you fling the weapon once with Hand of the Apprentice it will vanish at the start of your next turn.