Can a type be mentioned as an example in a concept, and not as an indication of what you want it to be?
During the Explanation section of a concept, examples of outcomes are allowed to be briefly introduced or briefly discussed. In reference to typing specifically, if the concept relies heavily on a single typing or only a few different combinations, then that is usually a warning sign that the concept isn't flexible enough. As such, it's usually best (but not required) to showcase more than one typing example in the explanation if a typing is mentioned at all. So, in short, yes, a type can be mentioned as an example, but only during the Explanation section. However, if the concept is incredibly rooted to a single typing, then that might be more akin to poll jumping and wouldn't be allowed.
Can you state moves in your CAP concept to use as support for it, as long as the concept doesn't specifically ask for said moves?
In the Explanation section, yes can use examples of moves for support. However, do note moves that define a Pokemon's role are allowed to define the concept itself. A recent example would be CAP22's concept, which revolved around the use of the move Parting Shot. In any case, moves in the Explanation section can be used to provide examples and support the possibilities of the concept. If providing examples of moves for a concept that isn't move-based (or providing examples for additional moves to a move-based concept) it is important to not mandate the usage of these moves and still show enough flexibility that the concept can succeed without these moves. For a crude example, if the concept is something like Weather Abuser, you could talk about using Weather Ball or Solarbeam in the sun, but you should not ever mandate these moves as essential and it is advised to show that the concept is not tied to these moves but merely has them as an option.
The basic premise for these questions can follow through for almost all competitive aspects of a Pokemon within a concept. The Explanation section has a ton of flexibility and allows for examples of typing, abilities, and moves to be given. That said, the general gist of the concept should be understood without the explanation (the explanation expands upon it, and in this expansion examples of specifics are allowed to be stated). The key here is not to try and force or mandate an ability/typing/move (or non role-defining move) into a concept, and rather to illustrate options. Also note that explanations don't even have to contain examples of moves/typings/ability (it's allowed, not required).
So, in general, showing examples of options is good, forcing a single or only a few options is bad. If you find yourself coming up with a concept that can only be achieved through a very shallow concentration of moves or abilities or typings, then that's a sign that it is not a good concept for the CAP project.