It's quite technical, but basically it describes two methods of constructing wood panelling that are partly see through (not solid). Fret work generally takes one piece of wood and carves (cuts) holes in it to make a pattern. Similar to the lace patterns. You might this separating a priest from someone doing confession in a confessional box. Spindles are individually turned and then joined to two or more other parts of wood that form a frame. Similar to what you typically find on a balcony or staircase. I guess the point of this in your text is that they are not plain, simple panels, but more expensive.

"Open fret or spindle work" are types of panels. Here it is referencing the way in which the panels were made. These are words associated with specialties, so I would not worry about knowing the definitions as I have no idea what the difference is.

This is an interesting question. FretWork is patterns of geometric shapes usually cut into wood. SpindleWork is often cylindrical work. Both are types of architectural or decorating designs. I hope this helps.

In this case, a spindle is a type of machine to do wood work on. A "spindle work panel" is a panel made on a spindle. Fret work is a different type of wood design using a fret saw. This passage therefore refers to two different types of woodworking panels. It is like 'carving' but the term 'woodworking' is better. Because it is woodworking the terms can only be applied to wood.