If you live in the US these products are probably easier to get but guys in Europe and Latin America might pay expensive delivery fees from the States. I think it's not a bad idea of sharing links to some of the online shops where you can find those products.
Most of the notions that I buy online in Japan come from Rakuten. Their mission is to become the world biggest online retailer.
What? Japanese silk basting thread
When? When working with tricky or soft fabric (velvet, wool, silk, taffeta). Sometimes you need to press the hem with the basting on it to leave a crease on fabric. In this case use the silk basting thread as it does not leave marks on the right side of the fabric. Often used in couture.
Where? Komadori, Yanagia, Sanoya, Aura. All these shops offer wide range of colors
What? Japanese cotton basting thread
When? This fine cotton does not slip and stabilized basted parts of the garment very well. For some reason, only Japanese know how to make this magic cotton thread ;) Great for tailoring.
Where? Handcraft, Osaihou, Ioki.
What? Fork pins
When? To sew together intersecting seams, especially if the garment has underlining or facing (say, wool on silk organza). It prevents fabric from shifting. You appreciate it especially when you work with prints that are difficult to match.
Where? Kanzawa, Handcraft, Yanagia, Ko-da.