1st time embroidering help

So, I bought a embroidery pillow case kit a week or two ago that I want to make for grandma, but I haven't started it because I'm unsure of the instructions on how to change or continuing with another strand of floss to secure it or how to end it. Is this method that it says really that secure for something that is going to be constantly used and washed. I just don't want the stitches to come out. Here's what I'm going to be making and what the instructions say:

I really appreciate any help. I really hope she loves this surprise. She loves embroidery and use to do so all the time, but I, unfortunately, don't think she can anymore. I can't wait to finish it and send it to her. She lives in another state and I can't drive it down, so I have to mail it. I wish this kit came with the embroidery floss. I unfortunately had to try to buy some and figure it out. The color key doesn't match up right for some reason. So, I'm changing the roses to red roses instead of red outline filled with pink. I'm also changing the cross because it says medium brown, but the picture shows more of a golden light brown and I'm changing the vines. There is a very light blue along the rose vines that you can barely see that looks like little leaves and also fills some of the bigger leaves. I'm going to change them to green. Seems like I'm making a lot of changes, but I still wish it came with the floss. I would've kept it as is if it had. I'm having a hard time finding the blues that I need. The blues I need, like the medium brown are not the right shades that the picture shows despite matching the numbers. Meh, I'm hoping I can get to one of the craft stores this weekend. I need more embroidery floss to do this because I can't find the right blues and I also need more embroidery floss for the Cuphead cross stitch as well as 18 count aida fabric. I only have 14 and 28 count fabrics which is weird. I thought for sure that I had more 18 count. Yikes! Sorry for such a long post.