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According to the Find Familiar spell description,

...the familiar has the statistics of the chosen form...

and

While your familiar is within 100 feet of you, you can communicate
with it telepathically. Additionally, as an action, you can see
through your familiar's eyes and hear what it hears until the start of
your next turn, gaining the benefits of any special senses that the
familiar has.

A spider's Intelligence score is 1. If my Wizard PC sends his spider familiar further than 100 feet from him, then once the spider reenters the 100-foot range, can it report back to the Wizard what it observed? Or does its low Intelligence prevent it from doing that?

Well, as you've noticed there aren't very many explicit rules about this, a lot of it can be -- and probably should be -- guided by what kind of game you and your players want. If that sort of easy scouting seems like it'll cheapen intelligence more than your table would like, I'd absolutely let that guide and flavor what exactly a spider can report back. Still, even if I were in your shoes and tempted to really rein this in, I wouldn't want the answer to be nothing, because that's not exactly enriching the table's game either.

However in the interest of getting more concrete, one thing you might not have thought of is looking at something like Speak with Animals:

You gain the ability to comprehend and verbally communicate with beasts for the duration. The knowledge and awareness of many beasts is limited by their intelligence,
but at minimum, beasts can give you information about nearby locations and monsters, including whatever they can perceive or have perceived within the past day. You might be able to persuade a beast to perform a small favor for you, at the DM's discretion. (PHB p.277)

To me, I would read this spell description as a pretty clear signpost that an Intelligence 1 doesn't mean something along the lines of, the creature has no sense of object permanence and is therefore unable to give any information about what's in a room, especially since locations, monsters, and within the past day are each explicitly staked out. The spell does not awaken or heighten an animal to humanoid intelligence in order to report all this, and so a low intelligence means a creature not only can still have some idea of these things, but must have some idea about these things.

However, I'd also absolutely have an animal be an entirely unreliable narrator, though not to the point of uselessness. Whether or not a spider can, left to its own devices, really distinguish between races of humanoids is probably something I'd land on no with. I'd probably also be tempted to think about what interesting ways a spider's perception would be inhuman and alien, and try to lean on that.

Yes, it can, but as a spider, it will provide very vague - if not barely useful - information.

The description of Intelligence in the rules states:

Intelligence measures mental acuity. accuracy of recall, and the ability to reason.

Telepathy is typically a one way link of communication. You can initiate it and perceive a response.

A beast is a limited Int creature that follows its own instincts.

Speak with Animals doesn’t directly coordinate with the telepathic communication. It confers a magical ability to understand the beast in its own natural forms of communication. This doesn’t mean you can teach it how to program a VCR to stop blinking 12:00.

A Ranger's companion is another reference towards interaction with a beast on a mundane level. Albeit a magical bond, it still is based off physically or verbal interactions. The beast will follow your commands to the best of its ability. So you can’t command the pig to fly, because the pig doesn’t naturally or instinctively know how to.

A beast outside of your 100 ft. range could only give you, at most, the vaguest of details that are barely useful, depending on the beast in question.

Some real-life animals can be trained to respond to situations in a certain manner, as well as actually having the intelligence of a young child and even self-awareness.

A spider is limited to its instincts and its senses. We have limited understanding about what a spider may think, but we have perceived what they can do.

Bugs and insects have inherent amazing abilities, but have very limited cognitive abilities, if capable at all.