Correct, they are a solid even though. If they maintain their shape outside of the container in which they are carried, they are considered a solid. They would only be considered liquid (at all) if you melted them down into a (I guess) jelly.
Yes.
However, as an example, hard boiled eggs used to be considered liquids/gels even though they will just glare back at you retaining their shape. Within the last year, TSA has seen the light and now consider hard boiled eggs solids

The TSA item look-up guide is quite useful (and at times a little entertaining). I also find it a good idea to double-check things close to a flight because the status of items and rules can change -- usually it is to be more permissive, but there have been times when things have become more restrictive.
SW