I dont' know about iron-on velcro, but I have used an iron-on technique with adhesive-backed velcro. Get some velcro with the regular adhesive backing, apply it where you want it, put a pressing cloth over it and ironing from the back side, use your iron to set it in place. Iron from the back side so that you don't accidentally melt the loops of the velcro. The adhesive will melt into the fibers of your fabric, and remain virtually indestructable. I know because once I put the velcro in the wrong spot and tried to move it! It wasn't budging! Good luck.

How tall are the kids, shoulder to floor? Say they are 3 feet...then buy 2 yds of polar fleece per child, then fold the piece in half so you have a doubled rectangle that is 1 yd long. Cut a neck hole ... A semi circle...in the center of the fold through both layers of fabric. Then cut a slit through just the top layer from the neck hole to the edge. You now have a robe with open sides. If necessary, you can cut the sides in to fit the length go the child's arms better...or it may be fine. Buy some cording to use as a belt to wrap around the waist to hold the robe shut. The beauty of polar fleece is it will not ravel. If you want to get more complicated, you can buy some fabric glue to glue the side seams shut, but not all the way up so there is room for the arms to go through.

On the seat cushions, if the cover is removable, try using a crochet hook from the wrong side. Poke the hook through the fabric, snare the loose thread and wrap it once or twice around the hook and then gently pull it back through. I do this on snagged sweaters and things all the time. The crochet hook can probably also poke some of the loose threads back in from the right side, where the snags are on the arms. Get a very small hook and be prepared to go slowly and use a lot of patience. I have sometimes seen a gizmo sold as a sweater snag repairer that would probably also work. If you can't pull or push the snags to the back side of the fabric, you can cut them. Then use the Fray Check that bac717 mentioned. A woven fabric won't unravel, the way a knitted fabric would. The Fray Check is just added insurance. My cats have totally destroyed one of my chairs. But since they have always confined the scratching to this one chair and will leave all the others alone, I just put the chair in my study where no one but me sees it. Why they have to attack the most comfortable chair in the house eludes me. But there is no more cording on the front legs, the stuffing is coming through on the side and even though I trim the snags regularly, those darned cats just keep creating more. (This is how I know that snipping the threads won't cause the whole thing to unravel. I'd have lost this chair 10 years ago if that were the case.)

If you have no plans to sew, Heat and Bond Ultra holds really well (I've known people to make t-shirts with that and it'll hold a couple of washes) It is thicker and not so great to hand sew through, there are other iron on fusible webs that are thinner and easier to hand sew through they will not hold as well. Glue hasn't worked so well for me, it can be messy/lumpy. For small pieces like that I'd probably iron on the fusible web to the fabric first and then cut small pieces. You then can arrange them however you want and iron to make it permanent when you're ready. Check out the art quilts of Laura Wasilowski, she fuses on tiny pieces. She has some tutorials on her blog and has her own techniques. She uses Wonder Under, which isn't so thick to do hand sewing. You definitely can play around with it a bit before buying a machine, but you will need to think of how you want to finish the project without a machine. You can frame them, hand bind, or buy a pre-made pillow case or blank to play around with. No sure where you live, but often Quilting Arts tv show will feature art quilters and techniques, or check out their magazine. Have fun! Here is a link that might be useful: Laura Wasilowski Artfabrik blog