Is twitter down TODAY after AP hacking?

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No it is not. The problem is at your end. Twitter is up and running. Checked just now.

REDIRECTING SITES are a CLEAR indication that ur computer is infected with malware/spyware/viruses.
Download Superantispyware, and AVAST. Install them and run them both. Remove any found threats and restart computer. Everything should be back to normal

Download AVAST from
http://download.cnet.com/Avast-Free-Anti...ag=mncol;1
On the lest side, click DOWNLOAD NOW. Install, run it-remove found threats.

Download Superantispyware from
http://download.cnet.com/SuperAntiSpywar...ag=mncol;2
Download it,install it, run it. Perform Quick Scan. Once scan is complete, click Show results-check all threats found and click Remove Threats.
(As a small PS- i choose Superantispyware over MBAM(Malwarebytes), simply because MBAM is not what it used to be, and Superantispyware actually cleans up where MBAM failed)