Healbot 1.126b4 I think is the latest functional vanilla iteration of the addon, it does not support absorbs or hots w. icons in the way you are referring to.
It will indicate the hot heal tick in the healthbars (basically showing heals from hots also)
but these ticks are usually tiny and can't really be seen easily.
It will not indicate absorbs, although some immunities will display the given healthbar as inactive (not out of range, just inactive/no aggro).
Features once set up include: range checking, combat/aggro/activity, healing indication, decursing/dispelling w. indicators, very responsive.
I've found some shortcomings to be: lacking hots/absorbs indication, no icons at all, no (low) mana indicators for others, no targeting through hb using ctrl/shift/alt+click (whyyy??), and perhaps the most important one is if you d/c during a raid/in combat and you log back in, healbot will not display bars/update untill out-of-combat again.
You could always give Grid Enhanced 0.11 a try, it has far more features at the expense of responsiveness, it seems to update around 100-200ms slower than the default UI/healbot and takes while to set up if you are not familiar with it.
This Grid version also has minor issues if you d/c, but this is resolved simply by getting back in range of the person/bar.
Personally I'm still not sure which one of the two is the "better" addon
they both have strenghts and weaknesses.
Here are a few screenshots of Healbot(left) and Grid(right) next to eachother.
I have little to no experience setting up Grid, so this may well be why I can't make it update faster or show heals.
Healbot bars are slightly darker than Grid in order to be able to indicate range/aggro/heals, aggro is indicated by the name turning from white to green as seen below.
Out of range indication (this was after a /realoadui which also causes grid to drop tracking till back in range)
Casting when clicking on Grid+Clique (in combat, aggro, in range)
Casting when clicking on Healbot (in combat, aggro, in range)
Edit:
Seems I was wrong about v1.126b4 being the most recent vanilla build of Healbot.
According to the v2.0 change log (Burning Crusade) there were two subsequent releases made before it.
Both versions contain some very nice fixes to the v1.126b4 that is floating around, but I have been unable to locate a working download link for either one.
So in a last attempt to get the latest vanilla version I wrote the author of Healbot to ask if he has a v1.1262 lying around he can share with us.
I will update this post if I ever receive a reply.
Change log:
v1.1262
=================
* Setting columns to 0 sorts columns by headers
* When casting, enabled bars remain enabled with only the text disabled.
* All localization bugs should now be fixed.
* A number of performance tweaks
* Added target to enabled bars, now possible to target while in combat.
v1.1261
=================
* Fixed dispell debuffs while targeting hostile unit
* Fixed incoming heals indicator while targeting unit being healed
* Changes to res monitor and incoming heal reporting, preparing for BC.