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Yes, I would. With minimal agitation.
I wash all of my fabric but with that small of a cut I would just wash it gently in a sink of warm soapy water and rinse good and hang to dry. good luck.
Yes, I would definitely wash it by hand.
I never pre-wash and I buy pre-cuts all the time (knock on wood) I have never had a problem yet - although I confess I've been nervous because I tend to use white as my background fabric - if you are nervous I would just put them in the sink and handwash them then let them dry - that way the shrinkage should be minimal.
Definitely not. What are you going to do if some of the fabrics shrink just enough that you can't get all the cuts you need out of them? Shrinkage is not an issue after the layers are quilted, especially if the quilting lines are not far apart, as the batting controls how much the fabrics can shrink.
If you are wondering about having a bleeder in the bunch, after cutting out your pieces place a scrap of each in a clear plastic tumbler of water and leave overnight. If it is a bleeder, you will see some dye leaking into the water. Take the damp fabric and rub it against any white or light fabric scraps in the kit to see if dye transfers that way. Chances are nothing will be a big problem and you can relax a little about dye bleeds.
If the tests show no problems, you are safe to do the first wash of the finished quilt in cold water with color catchers; just make sure you use a washing machine that uses *lots* of water so any small dye bleeds are sufficiently diluted. Also do not let the quilt sit damp after washing; transfer immediately to a dryer or lay out flat to dry.
If the tests show problems or if you have any lingering fear about bleeds, then use the same process as above for the first wash except use Synthrapol and hot water (Synthapol requires hot water to activate).
Okay, I will weigh in on this one. I have several mesh underwear bags in several different sizes for the pre-cuts' washing. I wash all my fabrics before I use them in quilts. When I started, I washed in warm water and those little charms shrank 1/2 inch on one side but not the other so then I started washing in cold water. With the latest invention of good quality cold water detergent, I can now wash them and they shrink ever so slightly if at all. So they get put in the mesh bags to wash and I lay them out flat on the top of the washing machine when they come out of a 5 minute trip through the dryer. When dry, I iron and starch everything after it is washed so they are given hot heat after washing. So, when I give a quilt, I let them know that that the quilt should be washed in warm/cold water. If they need to wash the baby quilt in hot water, who cares, the baby doesn't mind if it shrinks a tad and after all, they drag them around and they get worn anyway. My two cents.
Busy in Ohio
If they needed to be I would ( gently) if they felt funky, smelled funky or if they were ( bleeders) . check to see if the color bleeds, if so, prewash, if not I wouldn't worry about it.
hiding away in my stash where i'm warm, safe and happy
the only fat quarters, or fabric I get from a kit that I prewash are the red ones, and I do those in a sink.
I don't mind washing full 1/4 or 1/2 yard cuts - it's the fat quarters and other precuts that I don't wash. I normally do wash all my fabrics. In fact am working with a bazillion 1/4 yard cuts of batiks now which were all washed. However, coming from a kit - I honestly don't know what I would do. There is such a risk of running out of fabrics. When washing the fabrics after getting them on grain they are frequently quite skewed and you lose quite a bit when straightening the edge. You could always just cut one layer and start your straight edge on the short end of the piece as an alternative.