With the multitasking, its an issue that is showing up on all Sense 4.0 phones, including the One X. It seems that instead of the phone actually keeping apps open and doing work in the background or instead of simply holding the app open in a suspended (paused) state, the app reloads and you likely lose what you were working on.
As far as facebook pictures, this functionality worked flawlessly on all previous generations of Evos and Galaxy S phones. The phone syncs your contacts with their facebook picturs unless you manually specify your own picture to use with a specific contact. If I Decided not to use the built in texting app, 3rd party apps could show the synced facebook photo. In this version of Sense, the photos seem to be locked and not accessible by third party apps.
I won't comment much more on the contact pictures since I'm using the stock app and frankly don't have much experience with 3rd party ones, but apparently katmandoo122 got it to work on theirs, might want to look into that to see if you can use whatever method they used.
To answer some of the root related questions that you have though, first off, I think a big reason why the Evo 3D didn't get all that much support was because of the 3D, it apparently made camera drivers a bit hard to work with, especially when trying to port ICS to it. While the ImageSense technology might cause a similar problem I think it will a much faster fix for a few reasons.
1. The Evo 4G LTE has created a much bigger buzz because it's more of a successor to the original, not just an incremental upgrade with 3D thrown in. That means more developer support.
2. There are already at least 6 distinct ROMs on XDA, quite a few mods, a one click root method, and a custom bootloader unlocker. In well under 3 weeks. Many of them are progressing pretty quickly too.
3. It's already running ICS which make drivers less of a problem.
4. Drivers won't matter for Sense ROMs anyway, it would only create a problem (maybe) with stock ICS ROMs.
Now, I think there's a distinction between what the phone was meant to do and what the software it comes with was meant to do. For instance, the phone was meant to create a wi-fi hotspot, it's Sprint that imposes the cost on that if you stay away from rooting. As you've said, the phone was also meant to have true multitasking, it has more than enough system resources to do it, but apparently Sense locks that down a bit. Rooting, in my mind, unlocks the true potential of what the phone was designed to do, not necessarily makes it do things that it isn't supposed to.
From glancing over the XDA threads it looks like on the current build, un-rooting is no harder than rooting at the moment. If there's ever an official OTA you can still get that while rooted, and the update will probably unroot you itself. The apps that use root access don't generally require root access to install, but they will require it (and possibly superuser as well) to actually work as intended. Unrooting won't break the app itself, but you'll no longer be able to use the capabilities you had with it when you were rooted. Again, I think the developer support for this phone will be such so that even if you install an OTA that breaks your root, there will be another root method for the new version quite soon after it rolls out.
Also, I'd bet that fixing the multitasking wouldn't require you to flash a whole new ROM on there, I think it's something more likely to occur as a mod sometime soon.
Oh and somebody correct me if I'm wrong here, but I believe that Sense stops running in the background (at least after a restart) if you switch to a different launcher).