Since it leaps to a creature "of your choice", you don't have to target another creature if you don't want to

The description of the green-flame blade cantrip (SCAG, p. 143; TCoE, p. 107) has somewhat similar wording to that of chaos bolt:

You brandish the weapon used in the spell’s casting and make a melee attack with it against one creature within 5 feet of you. On a hit, the target suffers the weapon attack’s normal effects, and you can cause green fire to leap from the target to a different creature of your choice that you can see within 5 feet of it. The second creature takes fire damage equal to your spellcasting ability modifier.

Before the 2020 errata to the Sword Coast Adventurer's Guide, the relevant line of the spell description read "[...] and green fire leaps to [...]" (which is even more similar to that of chaos bolt); the errata changed that phrase to "[...] and you can cause green fire to leap to [...]" instead.

Rules designer Jeremy Crawford stated the following about green-flame blade in an unofficial tweet from November 2015:

What does the leap effect of green-flame blade do if there are no hostile targets nearby? Does it jump to allies?

The intent is that you can choose no one. If you can't see, you can't choose anyway, and the flame halts

Given the similar wording to the description of chaos bolt (XGtE, p. 151; GGtR, p. 67), it seems safe to assume chaos bolt would work the same way, so if there are no enemies within that range of chaos bolt, you don't need to target someone else.

This is even clearer after the update to the text of green-flame blade (due to the use of "can") - but even otherwise, the specification that it leaps only to a target "of your choice" seems sufficient to indicate that you can choose no target at all. The same logic extends to chaos bolt.

This makes sense to me. Given that if the energy of chaos bolt does leap to another, you choose what creature it leaps to, it makes sense that you can use the same control over targeting to prevent it from jumping to any creature (e.g. by having it fizzle harmlessly against the ground).

Hex Damage Applies on Each Attack

As you stated in your question, the description from Hex states:

Until the spell ends, you deal an extra 1d6 necrotic damage to the target when you hit it with an attack.

There is no limit to the number of attacks that you can apply this damage to, thus you can apply it to both attacks that you make with Eldritch Blast (or for both melee attacks if you are Pact of the Blade with the Thirsting Blade invocation)

As a reminder, on page 193 the PHB states:

Making an Attack

Whether you're striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.

And for further clarification on page 194 it states:

If there's ever any question about whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack.

As you are making 2 different attack rolls (one for each Eldritch Blast) these are 2 separate attacks and so you are able to add Hex damage to each of the rolls.

How the Dice Work

So from the examples that you gave in your question, assuming you hit both times:

• If you roll 19 and 19 on your attack rolls, you will deal 1d10 + 1d6 for each hit (EB damage plus Hex damage), for 2d10 + 2d6 total damage
• If you roll 19 and 20 on your attack rolls (in either order), you will deal 1d10 + 1d6 for the normal hit and 2d10 + 2d6 for the critical hit (doubling all damage dice), for 3d10 + 3d6 total damage
• If you roll 20 and 20 on your attack rolls, you will deal 2d10 + 2d6 for each hit (doubling all damage dice), for 4d10 + 4d6 total damage!

Hope that helps!