You will now work apply the armhole trim to finish your slipover. You will need to do this for both sides, but it doesn’t matter which you do first.
If they are resting on scrap yarn, you will need to put the 7 right or left (as needed) shoulder stitches back onto a spare circular needle so that they are ready to be worked. (does this mean I should put these 7 stitches on another 3 mm needle?)
Using a 3 mm [US 2.5] circular needle with a 60-cm [24-in] cord and starting at the mid- point of the underarm cast-on and working up towards the left/right shoulder stitches, pick up and knit approximately 46 stitches. (here I just need to pick up 46 stitches, not knit into them immediately, right?)
Knit the 7 shoulder stitches and then pick up and knit approximately 45 stitches working back to the mid-point of the underarm cast-on. Place a BOR marker between the first and last stitch you picked up. (how do I do this with one needle having only the picked up stitches?)
Yes, if you have another 3mm or smaller circular needle or double point, slip the 7sts to that needle. As you pick up sts you’ll be knitting the 7sts from that needle onto the working needle.
Picking up and knitting ia often used in patterns to refer to putting the needle into the opening of a previous stitch or row end, wrapping the yarn around the needle and pulling the yarn loop through to the front. It’s effectively “knitting” the stitch. No extra knit is required.
You’ll have 46sts + 7sts + 45sts on the circular needle. Now you’re to join the last stitch picked up to the first stitch picked up. Place a marker between the two to mark the beginning of round. You’ll be continuing to knit in rounds on these 98sts.
There are videos which show the difference between “pick up” and “pick up and knit”. Which might help reduce confusion. Salmonmac’s description is also really helpful.
I always find the pick up and knit row ends up quite loose and a bit ugly on my knitting. I learned a tip to pick up and knit with a smaller needle just for that first row to tighten up the join. It’s perhaps a bit too much to consider if you are unsure about what you’re doing but I found it so much more satisfying I thought I’d mention it.