Chill touch is not in the Basic Rules, it's in the PHB, page 221

Idea: Hook it onto an invisible creature to act as a big arrow pointing out its location.

"However, the most surprising use came when he managed to hit a Poltergeist with it. The Poltergeist has permanent invisibility, but he managed to make a wild guess as to where it's location was and hit it with chill touch. Now, they couldn't see the Poltergeist, but they could see the frikkin chill touch hand holding onto the bastard (The spell says the hand hangs onto the target). It completely trivialized the encounter. That one little bit of "flavor" text in the spell's description makes it amazing if you can managed to hook it onto an invisible creature."

Source: https://www.reddit.com/r/dndnext/comments/3x4rjq/no_cantrip_is_useless_examples_for_all_of_them/

Does Chill Touch shut down a troll's regeneration?

Possibly the most mis-named spell in the game:

Chill — Doesn't deal cold damage, deals necrotic damage instead

Touch — Isn't a melee/touch attack, instead it's a ranged spell

But the name fits the description of the spell. A chilling touch from a ghostly hand.

Casting Spellwords are:

Necropi Freezium

"Does Chill Touch shut down a troll's regeneration?" - spacewit

According to the spell's description, the target cannot regain hit points by any means until the caster's next turn.

So yes, this would prevent a troll from regenerating hit points for that round.

Would this spell stop a creature from gaining temp HP also? Could this stop a druids shape change?

yes

Gaining temp hp is not technically "regaining hit points"
It's up to the DM. But raw temp hp are unaffected. Since temp hp is not actual hp, but simply a buffer for damage

Just found out in an AL game yesterday that one does not need to have LOS to use this spell. After I used to attack a creature in a locked room, the other wizard in the part immediately abused it by sending out his familiar to get approximate locations of enemies and attack them with disadvantage. Most had like 10hp, but he killed like 3/5 of them before they killed his familiar!

EDIT: So I found that this use of the spell was wrong. I informed my DM, but basically -

A Clear Path to the Target

To target something, you must have a clear path to it, so it can't be behind total cover. If you place an area of effect at a point that you can't see and an obstruction, such as a wall, is between you and that point, the point of origin comes into being on the near side of that obstruction.

This from the basic rules helped me understand what was wrong here.

The main advantage though is that people can't see who is casting this spell since it creates the effect at a point. Thusly making it a pretty good sneak attack from a trickster or sorcerer.

It most certainly can! It's one of the loopholes you can use to take down trolls

They should have total cover if there is no line of site from the caster. It is a ranged spell attack, so total cover means it should always miss. If your DM doesn't mind, then that's fine, but RAW you need line of sight. 

Does Chill Touch shut down a Zombie's Undead Fortitude ?

Quote from Rayms_ >>

Does Chill Touch shut down a Zombie's Undead Fortitude ?

 Chill Touch would not shut down undead fortitude. Undead fortitude does not cause the creature to gain a hit point. It prevents them from losing their last hit point. It states that if they pass the save, they “drop to 1 hit point instead.” So on a successful save, they are not dropping to 0hp and then regaining 1hp, they are just dropping to 1hp.

How big would the hand be? I always think of it as being about the same size as the floormasters from Legend of Zelda.

Quote from thegreektrojan >>

RAW you need line of sight

 Would you accept being able to see the target in a mirror? Or would you demand the LOS be straight?  (Given magic is at play, I might allow an effect to curve.)

Also, given the damage is necrotic, wouldn't it actually be healing undead?

In previous versions, perhaps. But not in 5e. (I find myself saying that a lot!)

Does this line

"If you hit an undead target, it also has disadvantage on attack rolls against you until the end of your next turn."

Mean only disadvantage on attack against my character if I cast it or disadvantage on any attack rolls? Meaning if the undead creatures that I hit with chill touch tries to attack another character? 

Quote from Ryuma >>

Does this line

"If you hit an undead target, it also has disadvantage on attack rolls against you until the end of your next turn."

Mean only disadvantage on attack against my character if I cast it or disadvantage on any attack rolls? Meaning if the undead creatures that I hit with chill touch tries to attack another character? 

 Fair question, but it should be just against you. "If YOU hit...attack rolls against YOU." Expect to see "...and your allies" or "against it's enemies" if the effect was meant for more than the caster.