Regarding positioning the collar -
I have sewn a number of shirts, blouses and jackets in the way that you describe. Collars are generally always lined (and more often than not, and interfacing is added as well, but you can do without is the fabric will hold its shape). I find that collars usually lay better if the underside is of a slightly lighter fabric, but for a cloak that’s probably not a big deal. Just be sure not to use a heavier fabric.
I’ve been thinking about what I would do given your design. Because, I’m starting to think that i might need to spin for a cloak, too!
So, here is my recommendation:
Cut out two collars, fabrics of your choice.
Right sides together, sew the sides and outer edges together. But do not start the seam at the bottom edge. If you’re using a 5/8” seam allowance, start sewing the side 5/8” from the bottom (or whatever seam allowance you are actually using). And, you might want to mark he same spot on the other edge with a pin before you start sewing as a reminder to stop sewing 5/8” from the bottom edge on the other side. It’s easy to forget and just keep going and then have to pick it out.
Note: Patterns usually have you turn up a hem-sized section of the layer that will end up on top (that will show while wearing) before sewing the layers together, and then sew the layers together such that at the turned up part you are sewing through 3 layers. I used to follow that direction slavishly. But now I prefer to leave that part of the collar free in case I end up needing to ease it a little later on, which for me is usually the case. My way has saved me headaches. If you do it my way, be sure to backstitch at the beginning and ending of your seaming. And of course, do not sew the bottom edges at all. Also, I always go some backstitching at both sides of the points for reinforcement since one typically cuts off the seam allowance pretty closely at the point in order to allow it to be turned right side out (later) without getting all bunched up.
Now, turn the collar right side out. Mess around until it lays nicely and press it well.
Once turned, think of the “wrong side” of the collar as the side that will not be seen.
Pin the collar to the cloak such that the “wrong side” is hanging downward against the right side of the cloak. Make sure it’s where you want it. It would be a good idea to baste it in place to get rid of the pins.
If I read the other posts correctly, you are lining the cloak. If that is correct, then with the collar still hanging down, pin the lining to the cloak right sides together and stitch it. Do it just like you did with the collar: don’t start the seam at the bottom edge of the cloak. Decide how deep your hem will be and start there.
Your collar will be sandwiched between the two layers of the cloak (again, hanging down). When stitching the lining to the cloak, when you get to the collar position, you will be stitching through 3 layers: the cloak, the lining, and the “wrong side” of the collar where it is basted to the cloak. Be careful that you are not stitching through 4 layers. You want the bottom edge of the top part of the collar to remain free.
Turn it all right side out - the collar will reappear! Press seams well. Now, you finally get to complete the collar. Turn the unfinished edge under and pin it down (yes, you will be working on the top, or “public side” layer of the collar). Assuming that you have pressed the entire top edge of the cloak after turning it right side out, as you turn the collar under you will be able to match the position of the turned edge nicely to the edge of the lining.
Blind stitch the hem in place. I do this by hand. Voila. Done.
I would probably top stitch top across the entire neck edge (actually, I would top stitch down the fronts, too, after hemming is completed, because I like how it looks). It helps keep everything in place. But not all patterns call for it (though I usually do it anyway).