Welcome to the guild!
Just so you know there are Training Raids hosted by TTS 3 different times throughout the week. This calendar (http://ttsgamers.com/event-calendar/) goes by server time, or UTC. You can save it to your google calendar to convert it to your timezone if you wish. Also, as you can see, there are various times a week scheduled for guild missions and various, farmable open world events. Simply pick whichever training raid time, guild mission slot, or event set that best suits you (NA primetime, West Coast NA [aka Pacific, or PAC for short], or OCE - EU primetime events aren't currently active, and haven't been for some time).
As for dungeons and fractals, sometimes people advertise in their guilds for those. Not currently anything organized by the guild for those, unfortunately. PvP and WvW are in a similar boat, as TTS is a PvE-centered organization.
While I haven't been a leader for some time, I hope my information was helpful to you. Cheers!