As far as I know, nothing from the beta will carry over, except your new emblem/title.Looking forward to getting "Raiding party" with the 405th clan.
By my count, I'd have 9 of those achievements already if Beta gameplay counted towards it. Possibly more, depending on what classifies as a "raid" and/or "strike."
Raids and Strikes are very different. Strike missions are what the "devils lair" mission was. Raids were not in the beta and will be verrrrrrry long, which, confirmed by Bungie, will take hours to complete one, but you get some pretty sweet loot from them as well as achievements.
For Raids, you have to have 5 people from your friends list play with you, no match making, no randoms joining each other, strictly limited to playing with people on your friends list. Everyone in the clan should send friend invites to everyone else. There will be a thread started about a week before launch that will organize raids and we will also utilize the clan feature in the companion app/website. We won't be able to raid until end game, I think, which is level 20.