The first thing you need to figure out is if you want to make functional quilts that will be used as quilts or quilted wallhangings you can make for each family member as a remembrance. I honestly think some of those gorgeous pieces are only suited for the latter, especially the sparkly ones with many sequins. You also need to figure out if the sari fabric can take the heat from the iron to fuse the interface. I believe most sari are made from cotton but many are more like gauze type fabric. They should be ok. Where you can run into trouble are the embroidered fabrics as you have no way of knowing what the thread was made of. I would bet it is a mixed bag of silk, rayon and other synthetics. Then there are the sparkly bits, the sequins and such which probably will have no tolerance for the heat, even low heat.
If I were going to attempt this, rather than a fusible interface I would use starch. You can easily make your own out of corn starch or you can buy Sta-Flo liquid starch. But that would be a pain to transport back to UAE. I would research making your own and make it heavy so the fabrics once dipped and dried are as stiff as card stock. Then you can easily cut your squares, sew them together with no worries of stretching and the starch will make all the fabrics behave like they are same weight. Once your piece is all done layered and quilted you can dunk it in cold water to dissolve the starch. The only drawback to this method, is you may not have a functional (utilitarian) quilt when done.
Another option is to separate the ones that are questionable about handling heat. I bet you have enough that you could test each piece. Then use the ones that can tolerate heat and buy pellon 911FF fusible featherweight interfacing made for light and delicate fabrics or JoAnnes equivalent store brand, which is much less expensive but also not quite as nice quality as the Pellon name brand. That should stabilize it enough but keep in mind the interfacing will add weight to the final quilt as well as your beautiful sari fabric may lose some of its drape but you will have a utilitarian quilt that will stand up to normal use and washing. Save the real pretty sparkly ones for throw pillows or wallhangings.
Welcome to the board and I hope you come back to show us what you made of these stunningly beautiful saris.