If I have a block with multiple seams all come together in one spot I will press them open. Otherwise I try to do like Maniac Quilter does and pinwheel the seams open. One of the first quilts I started when I was a rank beginner I've recently finished and it has some seam nightmares--I plan to use lots of steam and my 3lb rubber mallet! :D

I also spin (or pop) seams where it is helpful... it allows the block to lay nice and flat.

Jenny Doan has a fantastic Hunters Star tute, no Y seams.

When the first two seams are nested, the cross seam should be pressed in opposite directions, so that all the seams rotate around the block. Your iron can go around and around in the same direction. That way when you sew to another block, all those seams will nest.

That center "pop" is easy to do. I grasp the seam with my thumb nails and pointer finger and twist. Most times and seam just "pops" open. Sometimes I can take a pin and undo one more stitch. But do not cut those threads. They need to stay there to secure the next stitch in that seam you just popped.

My stack 'n' whack was made that way, and it was very easy to sew one block to another. All the seams nested. Just be sure you go the same way on all your blocks; either clockwise or counterclockwise. I see in the pictures of OP that each one is different. The black and white goes one way and the yellow goes the other way. Works for her.

When I did mine, on the strips of opposing blocks, on one block press toward the star point and the other block press away from the star point. When you join the 2 blocks together you can nest the points. Then the long center seam I pressed open.
Also, because there is a fair amount of bias on these, when I have a wavy piece I spray with starch and hold a hot iron over it - not pressing, just heating. The bias wavy part will shrink back to shape.

I'm working on my son's Hunter's Star and this is just too easy. Also quick.

The tutorial on Cascade Quilts does not use Y-seams either. I made a block from MSQC tutorial and one from Cascade Quilts, and there are actually less seams in the one from Cascade Quilts. I like the look of it a bit better as well.

I have started pressing seams open. I've read a few articles on this issue, they say pressing to the side was to give added strength to the seams, but it was back when most quilts were done completely by hand. I started pressing seams open, and it works much better for me. I do a lil stay stitch at the start of each seam. I've washed a couple of my quilts, and so far they're holding up fine.
Good luck to you!
Kif

I plan on making one the Jenny Doan way. Hard to say when that will be.

I have made a Hunters star but I used a PP pattern, so much easier IMO