1. Modulator will take the "red/white/yellow" composite video and audio and turn it into a cable channel. You specifically want a "frequency agile" modulator (that means "you can pick the channel it uses"). Channel Plus makes a whole line of them; I use the 5545 and SVM-24. Each can do 4 channels and do IR control. There's a 5525 that does 2, and many other models to choose from.
Then, you need a device to combine two coax feeds, one from that unit and one from the cable company. I use the Channel Plus 8200 for that, which also provides power to the IR targets and relays the IR commands back to the modulator.
At each TV, I have 2133 targets (to hit with the remote controls for the DVD player in your case). The signal comes from the remote and hits the 2133. That puts it on the coax and sends it back to the 8200, which sends it to the modulator, which has IR emitters attached to control the DVD player.
Channel plus sells this all in a kit, the numbers of which I'm a little too time-pressed to look up, but some quick googling on your part should turn it up.
2. As long as you stick to high channels, you won't interfere with the cable modem, though you'll need to get the 8200-BID (bi-directional) to support a cable modem. Instead, I moved my cable modem to the basement cable entry and it's before all the video stuff.
Digital cable will cause a conflict if you pick the same channel that the cable company is using for their digital signal. (Note that the channels you see on the cable box, 852, 354, etc, aren't the actual channels on the coax; they're just a convenience for you.)
3. THe low pass filter is to block all the channels on the cable company feed to "clear out" some channels for you to use in the house. I knock out channels 69 and above (something approximately like that anyway), and I use the high number channels for my house channels. That does mean that a digital cable box won't work in the main part of my house, so if I had one, I'd have to put it in the basement and treat it like you're going to use the DVD player. (Put its output on a house channel, and cable its coax feed up before the low-pass filter.) That would also preclude getting many HD channels in HD, as the modulation is entirely SD NTSC.
If your cable company isn't using channel 79, 80 or 81 for their signal, you probably won't need the LPF and you can just get channel 80 overlaid onto your feed no problem. If they are, you'll need to find a spot where there's 3 channels in a row not in use, or you'll need to use filters.