pASLRB is not a substitute for the full 2nd edition rules, it is an accessory to it. How useful an accessory it is depends on your personal needs and habits.
No, it doesn't come with the chapter dividers. The chapter dividers that you can buy separately are the same as you buy when you get the full rules binder, i.e., they're out of date (they don't reflect the changes that came with HP). Currently the only way to get up-to-date dividers is the combination of those that come with the rules + the replacements provided in HP. Of course you also need RS to get the up-to-date Chapter G dividers. There is currently no way at all of getting the Chapter F divider, which was only ever supplied with WoA. As mentioned above, LFT's Rat Charts go a long way towards making up for this and should be considered as an optional purchase to go along with the pASLRB.
One of the most convenient aspects of the pASLRB is that it has all of the official errata for the chapters it contains in one place (including replacement pages) up to and including Journal 10. I recommend marking the affected rules sections so you know to look them up when required.
I wouldn't recommend continuing the use of the 1st edition rules at all. If you have them to look stuff up when you need to, a lot of the time, the things you are looking up will have changed in 2nd edition (although in most cases the changes will be minor). 2nd edition has been around since 2000, it's hardly new-fangled.