That "beam" would be called a ledger.
It should be held in place with big screws, use these in 4".
RSS™ Rugged Structural Screw
Two on each stud, dont burry the head. Make sure they are center of your studs.
Use these to hang your new joist ( when referring to joist, no matter if you have one joist or fifty, its always joist. Not joists.) In 8.5" you should have seven joist. Plus one top plate on each wall. Giving you a total 9 new joist to hold your floor. Seven can be hung off the ledger and the hangars. Like these.
APLH
The Last two I would sister into the top plates. This will require cutting the drywall.
Now we have nine joist sticking out and floating. dont count the first our the last joist. Start on number 3. Come in from the end 1.5" and attach your floor to ceiling stud ( post in the deck world). Do that on joist numbers 3, 5, 7. Now make blocks out of 2x4 that are 16" and tie all the ends of the joist together. These blocks will but up to the new stud (post) and be flush with the end of the joist. (That's why our posts are set back 1.5"
) now its looking like something right but it's not done yet cut one more 2x4 that is the entire length from joist 1 to 9 and cap all the joist ends and blocks with one solid piece of lumber.
Now you can lay your 3/4 plywood. Make sure it goes all the way back to where the roof hit the wall. You want as much nailing (use 3" screws, nailing is a term) as you can get. This will make it very strong.
As I'm typing this I get the feeling you wanna build this without busting and replacing drywall? While its ALMOST possible I would not do it like that. In that note tho, I realised that the three floor to ceiling studs don't need to be like that. For one you dont wanna bust drywall to tie into the roof and two the entire thing is in compression anyway.
So for those 3 posts, (now they truly are just posts, they're no longer studs) just come up 36" above the new floor of the loft and BAM, slap a 2x4 across the top. This caps the cut ends of the posts and is the hand rail for the loft. Just fill in with 1×1 every 2 or 3 inches and you got a fine looking deck rail!
Now we still gotta build an opening for your dang stairs so I'll have to see the stairs, top and bottom, diameter of the spiral and does the spiral even work at the height of your new floor...
AGAIN THIS IS NOT GONNA PASS CODE (although it might if you used 4x4 for the posts?) I never built a deck inside a house...