I'm currently playing in a rewritten RotRL campaign (meaning the new one for PF1). I've GM'd other campaigns using HL, but not this one in particular.
Short answer: yes, HL can accomplish all three of your tasks. Long answer? Keep reading...
My GM for this campaign has purchased the RotRL encounter pack ($25, IIRC) that includes pre-made encounters that includes all NPCs and/or custom monsters. We, the players, send him our characters and he combines them into a single "portfolio" (HL's name for a collection of characters into a party or encounter). Then, when an encounter occurs, he can import the party portfolio into the portfolio that contains the NPCs and monsters, and use that to run the encounter. HL does this using something called the Tactical Console.
The TC doesnt do everything, but it is certainly helpful! For example, buffs and debuffs can be done using it, although it can be cumbersome. For example, applying Cat's Grace is easy because it only applies to a single character, but Mass Cat's Grace is a bit of a pain, since the GM has to visit each PC and apply the change on the "Adjustments" tab (or maybe it's called something different on the desktop; I'm primarily using the iPad app as a player lately). Really, anything that applies to more than one character is a pain: damage via area of effect spells, movement penalties because of difficult terrain, and so on. (I used to use DMGenie back in the 3.5 days and it had a much better system for these types of things.)
There is also no automatic tracking of per-round spell effects. So short duration spells still need to be tracked "manually", so to speak.
I have a thread around here somewhere in which I've articulated the issues I have with how the TC works. My GM was frustrated by some of the above and we sat together for 4-5 hours one Saturday and jotted down notes of how it currently works and how he wanted it to work, then I posted here as well as filing those notes as a bug report (really more of a feature request, but HL only has bug reports; "for anything that you think doesn't work the way it should," which applies both to game rules and software functionality).
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I posted sort of tongue-in-cheek that I would write my own iOS app to address some of the issues. Well, turns out that I've actually been working on this, but it'll be my first iOS app so it's slow going. I plan to be able to import portfolios, but it'll only track the combat, it won't allow for leveling up — one of the items on your wish list. That will require HL.
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