What is meant with "near-equatorial" when it comes to orbits? Specifically, how many kilometers off the equatorial plane would a satellite in a near equatorial orbit cover? e.g. +/- __ km from equator.
I'm not aware of any single interpretation of the "near-equatorial" term, and if you search through the literature, we're left with several options. One thing is clear though, we're referring with it to orbits that have low inclination angle to the equatorial plane. Wikipedia on Near-equatorial orbit is rather vague:
A near-equatorial orbit is an orbit that lies close to the equatorial plane of the object orbited. This orbit allows for rapid revisit times (for a single orbiting spacecraft) of near-equatorial ground sites.
And marks that with citation needed. Indeed. Luckily, we also have a more specific definition of an equatorial orbit to work with. Equatorial orbits are considered non-inclined to the equatorial plane, so orbits with either inclination of 0° for prograde or 180° for retrograde orbits:
A non-inclined orbit is an orbit which is contained in the plane of reference. The inclination is 0 for prograde orbits, and π (180°) for retrograde orbits. If the plane of reference is the equator, these orbits are called equatorial; if the plane of reference is ecliptic, they are called ecliptic. As these orbits lack nodes, the ascending node is usually taken to lie in the reference direction (usually the vernal equinox), and thus the longitude of the ascending node is taken to be zero. Also, the argument of periapsis is undefined.
So we know this much, that "non-equatorial" cannot refer to "equatorial", or non-inclined. So inclined orbits then, but by how much? This is where it gets argumentative, and you'll get different definitions by different people;
One possible interpretation is that the term refers to those orbits whose ground track (projection of the movement of the satellite on celestial sphere from the orbiting body towards the orbital focus, i.e. nadir projection from the satellite's point of view, or zenith projection from ground observer's point of view) stays within the equatorial belt, so up to ±4° inclined orbits for Earth, if you consider the equatorial region as the area within 5°–8° Northern and 4°–11° Southern latitude of the equator. Of course, this will then depend on which body the orbit is at, and definitions of the stretch of their equatorial belt will vary significantly depending on who you ask. At planetary bodies with super-rotating atmospheres, it would make sense to describe the belt as the region of equatorial doldrums (e.g. Venus). And at bodies with no atmosphere, it would simply be some arbitrary value at a small degree inclination to its equatorial plane. And if even where equatorial plane is isn't clear and the body wobbles, it rotates on more than one axis, then you'd also need to adopt some definition of how prime meridian is selected.
So this above described option of how "near-equatorial" could be defined, while it makes perfect sense to me, also seems a bit ambiguous, or at least difficult to work with and non-intuitive, if inclinations of orbits around other bodies than the Earth are described with it. And that's perhaps why there isn't any strict definition to follow, and we usually mean with "near-equatorial" those orbits with low inclination to the equatorial plane, i.e. ±n° where n is, erm, small. And what low means to you, might mean something different to me or anyone else.
Alternative definition could be that they're orbits with large margin of error regarding their longitude of the ascending node, which is then given as for equatorial orbits to be zero, despite the orbital inclination not being exactly zero or 180°. You'd be looking at orbits with inclination well below 1° to the equatorial plane at Earth then, but this inclination might be larger around bodies where orbital perturbations (mass concentrations, secondary bodies, own orbital eccentricity,...) are, over time, more significantly affecting satellite's ascending node.
In other words, there isn't any single definition from an absolute authority source to adopt. What I describe is just one option, and my own opinion on the matter. It does somewhat follow the general adoption of the "near-" prefix when it comes to orbits (e.g. "near-polar", "near-circular",...) and it constrains inclination to a predefined region by ground track, if someone wants you to be more specific than low inclination orbits. But caveat emptor, my definition isn't authoritative in any way whatsoever. Don't use this as an answer to an exam question, or anything like that. Use whatever definition you were told to use by the one asking the question.
I always thought the term was defined by the relative influence of the 2 major forces perturbing a satellite's orbit. Namely:
The sun. The sun's gravity causes the plane of the orbit to rotate slightly with a period roughly equal to the 1.5 times the planet's year squared divided by the satellite's orbital period. For our moon this is 18.6 years.
The oblateness of the planet, which tends to push satellites into equatorial orbits.
Now, for our moon #1 is much bigger than #2, but for most our our artificial satellites, #2 is bigger than #1 if they are in approximately equitorial orbits. So their orbits do not rotate. If this were not true, then geo-synchronous satellites would be impossible, as the sun would rotate the orbit about the ecliptic, and the satellite would not be stationary.
So if the satellite is sufficiently close and is sufficiently equitorial, then its orbit does not rotate and it is a "near equitorial"; otherwise its orbit does rotate and it is not. My understanding is that the majority (but definitely not all) the moons in the solar system are near equitorials; the fact that the outer 4 planets are gas giants with huge oblateness relative to the earth is undoubtedly responsible for this.
Now, I probably don't have all this exactly correct; perhaps someone can clean up this rough definition. But I think this is the general idea.