Hi gfcdata and thanks for your attentions.

Redirects occuring when using IE and FoxFire
This indicates on presence on malicious extensions or plugin. Using IE and FF settings to remove unknown/unwanted extensions or plugin or using reset back to defaults would solve the problem.
Windows updates could not be loaded with error 80070216
Lately, a lot of malware intentionally deleted BITS service in order to prevent M$ to update.
"SFC /scannow" would stop consistently at 8% (even under Safe Mode)
If I'm right, this could repar BITS. I have not tested so I can not say...
Ran "Spybot" which removed several threats.
Spybot was once an powerfull tool, today outdated software.
Ran TDSSKILLER which found 2 threats which were removed.
TDSSKiller is ARK (antirootkit) tool, it scans for services and drivers (usercode and kernelcode) as well as MBR. In other world, if TDSSK detects malware, it means that detected malware is rootkit. Rootkit must never be taken lightly...