That’s a fine looking prayer rope. It does indeed look like it’s supposed to. Although, the tassel on the Cross usually indicates that it’s a Russian style rope. For the Russian style ropes, there is a bead every 11 knots on a 33 knot rope. On a 50 or 100 knot rope the bead would be every 10 knots.
Personally, when I make my ropes I like to have the knots a little tighter and to space them out slightly. But that’s just a personal preference.
I also suggest tying a strong joining knot before adding your final bead and tying the Cross. This is tricky, but worth doing. It requires you to use all four strands to tie a knot. It takes a bit of practice, but you’ll be glad you did it, and your ropes will be strong because of it.
Many Roman Catholics these days are purchasing and wearing prayer ropes. I have a number of Roman Catholic friends who have bought prayer ropes from me, and continue to wear and use them (and even give them away on occasion).
There is no difference between Eastern Catholics and Eastern Orthodox with regards to the use of the prayer rope or the prayers said on it.