I would like to know how to get the velvet-texture soft furry finish that is seen on some toys. A good example of this would be the Sylvanian Families toys (as pictured.) What materials and techniques are used and how could they be made without factory equipment if possible?
In short, flocking is the application of thousands of miniature fibers onto a surface. I'm fairly certain this is the general approach for what you are seeing on those dolls pictures.
Flocking is used to give something that velvety/soft appearance and feel. It's also very easy to do and gives your project a professional look. Flocking is used in a variety of different crafting genres, other than dolls, as well e.g. miniature terrain and bandsaw boxes.
Tools and materials
For this you only really need a few tools. Flocking fibres, some sort of applicator (optional but it really helps with uniform distribution) and a work space to contain free fibres. A very basic explanation is you paint or glue a surface and before it dries apply flocking fibres to the surface. Using paint of the same colour as your flocking can help give a uniform appearance and help hide the colour of the working surface and gaps in the adhered flocking fibres.
Typically flocking is applied as a single colour. For the sections that have multiple colours you would need to try and mask the areas you don't want to colour. An easier solution is to paint, where you already applied flock, in your desired colour.