1 looks okay.
2. I would include a comma after ‘In Moscow’.
5 is okay.
3, 4 and 6. Need recasting:
3)This week, former London City Police Chief, J.McGyver, will issue his findings from a three-year investigation into the cause(s) of Mrs Smith’s death.
(alternatively ‘has issued his findings…’ if he’s already reported on them within that week. Present tense does not work well because the actual reporting of findings would be one occasion out of the week.)
4)Several minutes before the accident at Furiani Stadium, safety officers had warned the spectators not to stomp on the floor.
6)The forecast includes a gale warning over the Channel and North Seas in the late afternoon and early evening.