What is the rough patch underneath?

That is the pontil mark. It happens when the glassblower breaks the hot iron rod away from the base of the finished vessel. Early makers left this scar rough and jagged. Later factories ground it out, leaving a smooth, polished depression in the centre of the base.

My grandmother left me a set with little silver spoons, but the bowls have this milky white film inside that won't wash off.

Salt is highly corrosive. Over decades it eats into the structure of the glass itself. That milky film is a chemical change. It cannot be washed off. Some people rub mineral oil inside to hide the cloudiness.

Why are some coloured blue?

The dark colour provides a sharp visual contrast against the contents. Before modern processing, table salt often looked grey or lumpy. Serving it in a rich cobalt or ruby vessel made the salt look whiter and more refined. It also helped diners see exactly how much they were pinching out.

I have a pair that look like tiny little bathtubs with flat bottoms and sloping sides, without any sort of feet or stem attached to them.

You are describing a trencher salt. This form sits squarely on the table linen without a pedestal or legs to raise it up. They were popular in the eighteenth century. Diners would place them next to their wooden or pewter trencher plate. The low centre of gravity meant they rarely tipped over during a busy meal. Glassmakers usually formed them by blowing into a mould and then cutting facets onto the thick sides.