US WoW Servers weekly reset happens at 08:00 AM Pacific Time, every Tuesday.
EU WoW Servers weekly reset happens at 08:00 AM Central European Time, every Wednesday.

WoW US daily reset happens at 08:00 AM Pacific Time.
WoW EU daily reset happens at 08:00 AM Central European Time.

Weekly reset gives us clean lockouts for various content in World of Warcraft such as: Raids, Dungeons, World Bosses, Mythic Dungeons, Weekly PvP, Pet Battle Dungeon, Legion Archeology.

Daily WoW reset clears saves and gives us new: Daily Quests, Emissaries, World Quests, Normal and HC Dungeons.

They are.

Have in mind that local times may increase or decrease the time by an hour at two points in the year due to daylight savings time changes.

To check your current raid lockouts press your 'O' key in-game, select the Raid tab, and click on Raid Info in the upper right. This will display your current lockouts, and time left until they reset.

You can also use the addon for this.

WoW World Quest reset time is basically every 6 hours. The biggest reset is typically at the daily wow server restart time. and 6 hours timespans also count from there. WQs are generally always up for at least 24 hours though, so if you clear them all daily, you probably don't miss any.