I have the same model that you have and I have only had the first issue.
I purchased my EVO Design in January 2012 and have noticed that (depending on the cover I have on it at the time), I have the issue with the screen going dark during a call. Normally, the screen does this as a "power saving" option. However, I've found that if I have the phone on speaker, it does not go dark (and the sound quality on both ends is acceptable). I've also found that if I hit the "On/Off" button on the top immediately after initiating the call and it goes dark, it will light up for about 3 seconds, long enough for me to put the call on speaker phone and then the phone stays lit up during the call. I currently have a bulky cover on it for protection and this is the cover that I see this issue with the most. My smaller covers (usually the small silicone covers) do not so this issue near as often as my big bulky Kingdom Hybrid case does.
I have not had any troubles with the battery life of the phone (other than it dies within 10-14 hours of removing it from the charger due to usage) and have not had any trouble with the camera not working.
However, my most recent issue with this phone has been over the last 10 days. I'm not sure if it is Sprint or HTC, but someone is doing updates/maintenance in the area and my service has been outrageously inconsistent. Approximately every 10 seconds I receive an error message on my phone that simply states "Data Call Failure". Doesn't seem like much, but this means that I'm not receiving emails and cannot stream Pandora - ie. My data service is non-existant. I'm furious with this as I listen to Pandora daily and being out of touch with my email is unacceptable. I have been in contact with Spring Tech Support 4 times over the last 10 days and their answer is (this is my translation of what they're saying) "we know your phone isn't working, we can't fix it, and we don't know when it will be working again". This is VERY frustrating to me, but they're not pointing fingers or taking responsibility...
In short - no, I do not believe that this is an HTC problem or a Sprint problem. I believe your issue was actually with the specific phone (not even the model) that you had.