If you're good with technology and computers, and exploring the menus is something you'd do on your own anyway, you'll catch on very fast. Before the end of my training, I was teaching my PD nurse some things about the cycler.
The Liberty has a battery backup, but not an active battery. When you unplug it, it won't stay on, but it should remember where you are in the process and restart at that point, after telling you it went through a power failure. There are 3 to 7 connections to be made, and the bag connections are on short lines, so if you want to do all the setup in the bathroom, you'll have to roll the cart in there and switch power outlets.
The drain line is integrated into the cassette with all the other tubing. There are different cassettes with lines of different lengths - I have the 20-foot drain and patient lines, which let me drain into the toilet, and make it to the bathroom myself if I need to. All the lines are actively pumped during treatment, so the drain line should be able to be snaked around whichever way, as long as the end isn't too high above the height of the cycler.
One of my cats is interested in the bubbles in the drain line. She waits outside my door for me to set up the cycler and run the drain line, and then she sits and watches the bubbles as the line flushes. I don't think she's tried to do anything bad to it yet, but even if she does, the drain line is a one-way thing. Since it's pumped and separate from the other lines, nothing that happens to the drain line can give you peritonitis (nothing that's at all likely to happen, anyway).
The machine isn't loud, in my opinion. It will make noise only when it's pumping - you to drain, heater bag to you, or other bags to the heater bag. If you can tolerate a fan going while you sleep, the cycler probably won't pose a problem. I'm a relatively light sleep, and it doesn't wake me up.
The alarm is louder than I'd like. The volume is adjustable, but the loudest setting is ridiculously loud (like wake up the whole house and your neighbors loud). I use the lowest setting, which is loud enough to wake me up with the first beep, and my mother in the next room (she's an extremely light sleeper, though). You'll see what it's like when you try it out.
You can get alarms for a few different reasons, but the most common reason to get an alarm while you're asleep is, yeah, you rolled over onto the line, or you're sleeping wrong and the catheter isn't positioned well inside you and you don't drain enough. When the alarm goes off, you hit the stop button to mute it, and read the alarm message on the screen, then fix whatever's wrong, then hit the OK button to continue.
If you roll onto the line enough to kink it completely, you'll usually get an alarm right away. I often roll over just enough to restrict it somewhat, but not enough to trigger an alarm, and it drains or fills much slower and then alarms when it reaches the drain/fill time limit and hasn't reached its goal. Same thing happens if I'm lying on my left side - it can't drain enough because my catheter is too high inside me then.
One more thing that got me the second night I used the Liberty: if the second dialysate bag is sitting somewhere that somehow restricts the pumping from that bag, you'll wake up and find yourself not nearly done. When the cycler finishes a fill, it will start pumping from the second bag to refill the bag on the heater. If that line is restricted and the refilling goes very slowly, it won't alarm (at least it didn't for me) - it will just keep trying to refill the heater bag, and stay on that same dwell. That means you might stay on a single dwell for hours. Just make sure you position the extra bags well.
Any other questions, I'll answer them if I can.