"In case of termination for bad performance, I am not getting severance pay for my 8 years of service, right?"
Very few states require the payment of severance. If your company offers you severance pay when they terminate you take it.
"How this termination by poor performance would reflect on my future job search?"
Compared to the number of people searching for jobs probably not much different than anyone else.
"Should I forget about questionable unemployment benefits and quit myself to avoid "bad' record in my employment history?"
Bad idea. Some money coming in is better than none. If you quit you will definitely be ineligible for UI. If they do actually terminate you for poor performance you may still be eligible for benefits and collect them. Most likely you will in this climate as it shouldn't be viewed as gross misconduct. Given the scores of people who have lost jobs you will be a blip on the radar screen of people filing for benefits and searching for a job under the circumstances you were terminated under.
"That's just my opinion, then again I might be wrong." Dennis Miller