I love to add to my pillow cases, my best tips are, keep your stitches short, start and end with knots (I know to some this is taboo but if it goes in a washer on regular this is the only way to keep it form unraveling), Avoid satin stitch like its the plague, it never lay right after its been threw a spin cycle. And my biggest tip make sure its stretched super tight on your hoop. Thats how my many embroiderd pillow cases has stood the washer many times.
I <3 thread heaven, I jut hate that ) keep losing my little box of it. And to answer the above question about what it is; thread heaven is Silicone, And my advice about bee's wax is if its not yellow it's not bees wax, I have noticed that with the sewing notions everywhere there are supposed blocks of bees wax in a cute little plastic holder, but after buying one and running thread threw it I discovered it was just paraffin wax, the thread nearly cut the thing in half, that never happens with real bees wax so if I want wax, (I only use natural stuff when making things for kids) I buy a brick for candle making a break off a large chunk and keep it in a little draw string sack.
Now the second part of the question, no bees wax and thread heaven should not change the color of your thread, and have not on any of the standard floss I have used, they don't work well on metallic threads I ave heard but I have not tried that so I that I don't know.
May have been your stitches, if the tension on the cloth while you were embroidering it was to lose this can happen; I know every one on here is thinking its the floss, but I use cheap'o floss Sullivan's(the stuff Hancock's sells now), and the 36 or 110 packets of six strand stuff you can get for like $3.99 at craft stores, and I have *knock on wood* any of it to shred in the wash, and I sew on every pillow case I own, and most are just 180 thread count some are even less, like 120. I know your not suppose to do this but when I know something is going to get washed I start and finish it with knots, I make my knots in a particular way, after your last stitch go back under and make a loop and then go threw the loop makes a unnoticed knot, I also tack down all my satin stitching with something decorative on top even if its the same color. But really you should wash things on a hand wash and in a net washing bag. I wish you would put up a pic, I have lots of experience with these issues.
I know the secret to getting them off! when your embroidery is finished you hand wash it with IVORY or a bar of castile or fels naphtha, but Ivory, and kirk's castile bar soap work best and give it the good ole scrub with lots of soap, nice and lathery, repeat a few times if you need to. I always make my stitches are finished well when I know I'm going to do this. This will work most of the time unless you have put it in the dryer, at that point its on forever.
I own a bag I got at target a few years a go that's JUST like your bag, its reversible, and the tie on it is made of seem binding sewn together, I use the tie all the time. In the city you need to be able to keep your purse closed, to keep people form pick pocketing you.
this sounds stupid but I don't go in to any project with a game plan... what I tell my friends who are learning form me is, go crazy if you think you want to do a stitch and it looks bad in the end you can take it out, but you might just want to leave it in... things in the end can look really good with your experiments, even if you don't think so.
And realize that this can go from a hobby to a obsession very fast... I don't own a sheet or pillow case, or shirt that does not have some decoration I added to it.