I just started using C Locker, which pretty much offers everything you're asking for. Let me list some of the things I think match your request:
- Free: There's a C Locker Free with minor limitations (not affecting any of the features you're after IMHO), and there's C Locker Pro with some advanced features added (and the ads removed, which in the free version are visible in the configuration screens only)
- Offers a good deal of customisability: If not that, then what? The "C" stands for "Customizable" (and for "Convenient"). Tons of features, like including weather, clock, and more on the lock screen, customizing the "unlock wheel" (unlock-and-start-app), and I love the "light-bulb" symbol in that wheel to quickly turn on the torch when needed.
- Has an integrated pattern unlock: Want it always? Or only for certain shortcuts? Or for all but X? Up to you, just configure it :) (must admit, I didn't try this part yet)
- Shows phone, SMS, and music notifications/widgets to some degree: No degree. All you want. Well, almost. I currently can directly start two camera apps, the flash light, mail, telephone, and have 3 more left I didn't use yet. Has multiple lock screens which switch automatically (context sensitive): You have your normal lockscreen ("Standard"). As soon as you start music, the "Music Lock" is used (with the player widget). You even can have multiple location-based screens: one for the office, one for home, whatever you set up.
- Does not require you to install a launcher with it: Didn't ask me for that. Still using my custom launcher (Apex)
- Can be for rooted phones only: Not really required, but if your phone is rooted, it supports some extra features – such as making it a system app
Disadvantages? Minor so far. I've used the free version for a day, then straight went to buy the pro. Turning the screen on, it took several seconds for the lock-screen to show up its controls. So I've made it a system app. Still takes a little (maybe 3 secs), but got a little faster.
All in all: I don't think another locker can come up with that. So: top five, recommendation :)
Finally, some "visuals":
C Locker: Music controls, a custom lock-screen, the "unlock wheel" (source: Google Play; click images for larger variants)
In case you wonder: the "wheel" you see in the third screenshot is, by default, invisible – and shows up as soon as you press-and-hold the "locker" symbol in its center (and then draw it to the action you want to perform). But as almost everything with this app, that's (C)ustomizable :)
Oh, PS: In the "about" section, Cheah (the dev) links to a lot of helpful youtube tutorials showing your tips and tricks to get more out of the app…
Apart from that, I just "scratched the surface". Lots of other things I didn't mention, like gesture control, one/two/three times tapping a widget, and more. Just check it out, there's a free version!