I was looking at the suggested cameras on Amazon, and judging by the user-uploaded photos, I think that I am currently favoring the
Canon Rebel XTi.
Bear in mind that the lens is more important to the image quality than the camera body, and the photographer is even more important than the lens - I'd rather have a cheap Nikon body with a high quality lens than an expensive Canon body with a cheap lens.
1: During film productions, I almost always use some sort of Tiffen filter, like a ProMist, for example, or at least an ND filter of some sort. Are there filters compatible with the Canon? I don't believe I've ever seen a matte box holding one on a still camera, so I assume it screws on to the end of the lens or something? Would I look for a compatible thread size when shopping for them, or something else?
The first type of filter you can get is a circular, threaded filter. These come in various sizes, and this is the type I would recommend for UV, circular polariser, neutral density, and colour filters - ie, any filter with a uniform effect across the entire shot. I have four lenses, with three thread sizes: 58mm, 67mm, and 77mm; I also have step-up rings to allow me to mount 77mm filters on all of them (because a circular polariser is so hideously expensive for a good quality one, I only have a 77mm polariser.)
The second type is a filter holder of some sort; Cokin P series is the most common of these (although by no means the only one.) These consist of a filter holder, and usually an adapter ring to mount the holder on the camera lens. I have a P series holder with a 77mm adapter ring; if I need it on a different lens, I use the step-up ring to do the job. This is the type of setup that works best for gradient filters; it allows you to move the line between the clear and neutral density portions of the filter according to the needs of the shot, rather than having it go through the middle of the image.
Note well the difference - circular filters for constant neutral density filters; filter holders for neutral density
gradient filters. Given your background, I don't think I need to expand further on this.
2: If I do end up purchasing this Canon Rebel, am I limited to Canon lenses? Or are lens connectors universal? The reason I ask is that a studio I work with has a huge, diverse collection of some pretty great Nikon lenses that would be fun to use, but I don't know if they would fit on the Canon. If I can't just use any lens on any camera, what do I look for when shopping for lenses to make sure it will work with my Canon?
The answer here depends on who you ask. Canon will tell you that third party lenses may damage your camera body. In reality, Sigma and Tamron (amongst others) have reverse engineered the Canon EF mount, and manufacture their own glass to fit Canon bodies.
As for Nikon glass: the design of the EF mount is such that you can obtain a physical, mechanical adapter, and mount lenses designed for almost any other lens mount on a Canon body without any issues beyond losing autofocus ability, and possibly aperture control (depending on the lens and adapter). The major exception is the obsolete Canon FD mount, which requires an adapter with optical elements to allow focus to infinity on an EF mount body; Canon used to make these, but they were intended for pros with high-quality FD glass; you would struggle to find them second hand.
In terms of official Canon glass, there are two lens mounts of importance: EF, and EF-S. EF lenses are "full frame" lenses, designed to cast a circle of light to cover a 35mm sensor (negative, slide, or digital sensor of identical dimensions to a 35mm negative). These will mount on any Canon EOS body, digital or film, without issues.
EF-S lenses are designed specifically for Canon EOS digital bodies with a 1.6 crop factor, and will mount only (as I type this comment) on the 300D (Digital Rebel), 350D (Rebel XT), 400D (XTi), 20D, and 30D. If you think you are likely to move to full frame photography (film or digital) down the road, you would probably be better off spending your money on EF glass, but the EF-S focal lengths tend to be more useful for a lot of people on the 1.6 crop bodies.
A couple more data points about Canon's lineup: the highest quality lenses are the L series lenses (L for Luxury), but you pay through the nose for them. These lenses are always EF mount; Canon has stated that they will never make an L series EF-S lens. However, the EF-S 10-22mm (extreme wide angle) and EF-S 17-55mm f/2.8 are L series quality in terms of their optics, and hold their value very well; the differentiation, for them, is marketing, and the quality of the physical body holding the elements together. The other EF-S lens I'd recommend is the 17-85mm. The 18-55mm tends to be underrated by most serious photographers, and can (and has) taken a lot of excellent photos, but the step up from it to the 17-85mm is noticeably improved in image quality. The 17-55mm is better again, but as always, you pay a price for that step up. Your money, your choice.
Don't bother with the EF-S 60mm macro; you're better off with the EF 100mm macro, or a Sigma 105mm macro, if you want to do macro photography.
Having said all of that: if you have access to a large library of good Nikon glass, I'd recommend a Nikon body, and that you follow the advice others have given in this regard about which one to buy (I wouldn't know - I shoot Canon). Much less hassle, and you won't have to spend as much money building up your lens collection. There's very little in the Canon world that you can't do in Nikon, and the reverse also holds true.