That's 3 questions ?
1/ Everywhere in Mindanao except the western side is as safe as the rest of Asia, Siargao would be one of the safest places in the country. You will be fine there.
2/ The weather should be fine during that time, there is an international pro surfing event held there in August so if you are there then expect to see lots of people.
3/ One week would be great, you would be able to see all the sights, including the island hopping tour (highly recommended) and still have a day or two of just relaxing.
Siargao is one of my personal favorite places in the Philippines. The island is beautiful and the people there are so friendly and laid back, you can't help but relax and start working on 'island time'. Go enjoy yourself
source:
www.tripadvisor.com.ph/ShowTopic-g674645...ovince_Mindanao.html