The prince definitely seems to have died, at least judging from a good number of online reports from Arab world publications, such as:
http://gulftoday.ae/portal/326349c6-e994-44c3-b7b7-da29fa3a83fd.aspx
However, the video posted on LiveLeak definitely seems to be a hoax (well a real video but unrelated to the prince). I have not seen anything that appears to be reliable which says either that the prince committed suicide or that he had been ordered to leave the UK and return to Saudi Arabia.
So his death seems pretty sure but I don’t trust any of the details yet.
I saw that video and thought “That doesn’t look like a 69 year old guy doing that...”