Since this sounds like an art piece, are you seriously considering a lot of laundering of it in the future? Most people who do art quilts know that they won't be laundering them as opposed to regular functional quilts for warmth. May I suggest that since you don't own a sewing machine and don't have the usual quilters' tools, why don't you just buy a few fat quarters and some fusible web and play around with them? Since you are fascinated with the mini mosaic concept I'm sure that you will create some wonderful things for art's sake but the labor involved will prove to you that you won't be wanting to make quilts for comfort like this that need regular laundering. I've done some art quilts with fusible and yes I embellished them with machine quilting, too but I wouldn't dream of using these pieces as regular quilts.

Starting with things that don't require much washing is a great idea. I could even do things that aren't quilts like decretive pillows. That way I can experiment with hand stitching or even entertain the idea of a small sewing machine after I've done enough projects to justify the expense of the tools.

Does anyone have any experience with e6000 stitchless? This looks like a good option because the glue would hold the small pieces in place, meaning I could layout a few rows of squares before ironing.

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