Vtyjkyuk

Supposing my wizard has an owl familiar (120ft darkvision) and spots a band of enemies 120 feet away at night. If my wizard engages from a distance that they cannot possibly detect her from, is a surprise round guaranteed?

The rules on this are very short:

The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side.

The DM might reasonably decide that the distant owl (or wizard) is too far for any check to be required — there's room for that under the first sentence of the paragraph. But there's no guarantee. Remember too that what is good for you may work in reverse, and that if this is what your DM decides, it's totally reasonable to also sometimes have the party entirely surprised with no chance to not be even with high passive perception.

In a situation where it's just a very small, stealthy creature that is likely to be in the environment anyway, like the owl alone in a forest, I might as a DM forgo a check, but 120 feet isn't really all that far away (especially when you're talking about heroic characters and their elite and perhaps mystical opponents). So, to resolve any doubt, I would probably require the stealth check — which the owl is quite good at, anyway — and apply an appropriate penalty for to the opposing passive perception. Maybe the owl catches a glint of moonlight and a very perceptive observer catches on, or whatever ranged attack the owl is about to make (a spell?) causes something noticeable just in time.

If the wizard sneaks up to cast fire bolt, though, the check seems absolutely warranted. The situation would have to be a lot more in her favor for it to even occur to me to have her automatically succeed.

The official rule is "DM determines surprise". It is up to the DM whether they require any kind of roll before declaring that any characters could be surprised (as pointed out in other answer, there is not really such a thing as a "surprise round" in 5E, although informally it can be thought of as the first round where some of the characters can be surprised).

It is rare that any strategy is perfect though.

For a start, your character's owl is not guaranteed to spot all foes at the limit of her vision unless the encounters are happening on a featureless plain. 120 feet is close enough that enemies could hear movement, and they would very likely see lights from torches etc, so you'd better all have Darkvision or be well hidden. In addition, outside at night is rarely perfect darkness.

Assuming all that is good and DM has told you that you have noticed the enemy, but they have not noticed you, then you still have an issue. Unless the owl itself is going to deliver the spell then your wizard needs to be able to target the enemy somehow themselves. That will usually mean approaching the enemies and/or preparing an ambush, unless your wizard already happens to be standing with clear line of effect from themselves to the target - i.e. they are standing, in the open, within 120 feet of the enemy, and with nothing between them and the enemy. They will have needed to be in this state whilst the enemy did not notice the wizard at all, and with the wizard likely unable to tell in advance whether they were standing in a good spot.

Stealth or Deception are commonly required in order to set up an ambush. Depending on circumstances (such as amazing recon done by a familiar) might give you Advantage or even persuade the DM that no roll is required. It will come down to individual circumstances though.

A simple scenario where I would as DM grant absolute surprise with roll for your setup: It is a very dark night, or perhaps underground. The wizard is standing guard for a specific location, and not moving, with line of effect to where the enemy is approaching from. The owl is flying more or less directly above the wizard's head to help them take guard, and otherwise there are no good clues to the wizard or their allies' presence. Then I would probably just declare that the approaching enemy all were surprised in the first round due to the large difference in perceptions of PCs versus NPCs. If the night was not very dark, then I would allow even enemies without Darkvision to make an opposed roll versus the Wizard's Stealth or Deception, because normal people can see things 120 feet away on a typical moonlit night. The enemies' rolls would likely be at Disadvantage.

There is no surprise round in 5e. There is a surprised condition. Initiative is rolled as normal, but the "surprised" creatures cannot move or take actions or bonus actions on their first turn of combat and may not make reactions until after their first turn ends. If they were expecting or preparing for an attack then they wouldn't be surprised, however, the circumstances make that seem unlikely.