Most tourists visit Turkey between April and November, as in winter it can get very cold and rainy. Summer is also very hot in some areas, so maybe you should avoid Mediterranean and Aegean part in July and August, unless you are planning to enjoy nice sea and beaches in these regions.
Istanbul, Turkey's largest city, and Ankara, its capital, are as safe as any other big city in the world. Most terrorist attacks usually target Turkish state, but no significant events have been reported in the last 2 to 3 years.
It depends on the part of Turkey you visit. In western part of Turkey - Istanbul, Mediterranean and Aegean coastal areas, you can wear whatever you want. Central and eastern Turkey is more conservative, so you should definitely avoid revealing clothing. Wearing appropriate clothing and a headscarf is appreciated in mosques.
