Sorry, I mean the HDTV LG 55lb6300.
So, in order to answer all your questions, I have to say that I am not a 100% experienced person regarding webOS, but from what I know(reading webOS forums, searching the web and studying LG's website) there is no such thing as a custom webOS for LG TV's(but I also might be wrong). Please take in regard that your TV is a discontinued one, so this means, it will not get any further updates.
1. The latest updated firmware for your TV is version 5.00.55 released on January 25th 2016. You can check your webOS version in the Advanced Settings-> About this TV
2. No customization regarding GUI(except for ordering apps) - we are a long way from customizing on webOS.
3. I think you found them yourself. No quick web browsing. But if you have a magic remote, that's the quickest you can get with browsing .
4. You can, if you have AN-MR600(the type with 0-9 physical buttons on it) and if this model of remote is supported by your TV.