It's very hard for me to put words to how my conscience works. Part of the problem is I actually largely do not think in language. Because of that I can only describe it by relation; and that can be inaccurate at times. I can start by stating that I do not think in language. I think in images, feelings, concepts, and general ideas. I can think of an entire storage list of information, maybe a paragraph in a book, without "thinking" a single word. When I need to retain a string of numbers, I will not be able to if I try to "think" the numbers in an order, even saying it outloud sometimes will cause me to fail. Instead I half imagine the physical shape of the numbers in my head, and the "feel" of the numbers. It remains in this limbo state in effect, where I am just about to actively "think out" the number sequence. I can see and "feel" the numbers, but not think it. Once I write down the numbers or recall them, they can be lost. However, this "loss" is not permenant in some cases. If I "forget it" for a period of time, my mind can work it out in the back of my mind (my subconscious really, but I digress as that is not the topic of discussion right now), and hours later I could recall it.
This simple example is how I recall, remember, and think in the majority of cases. Much of what I think feel say and do remains in this psudeo-thought state where it is on the border between being verbal, visual, felt, or another unknown mode. The second I drift into one of these and extract it (I need to externalize it into one mode in order to get it out), I can explain it and process it. Sometimes I am not aware that I am doing this. If I pay attention I can "recall" where a thought or idea came from. This act of translation between extracting information from my conscious (and what I assume to be subconcious as well, I could be describing that at the same time) is why I can appear lost in thought or scatter-brained (which is largely a misnomer, although I will say I am at times for ease of others to understand). This is also why I say I am a slow thinker. I think very intensely and deeply about pretty much everything, but there is a high volume of material to go through.
I actually don't have complete control over how I think. To me things often "come to me out of the blue". This is because of the afformentioned way in which my thoughts remain in a limbo state in a sense. The act of recalling and understanding something is fast on an internal level. Things can very quickly fill this room, getting it out of the room is the slow part. That slow part I have control over. However as I in effect did not "choose" to put all the information into that room in the way that I did, I in effect did not actually control how I thought the idea in the first place. This can be frusterating at times as I can sometimes become irratated with myself with the inefficency of this information. More in the act of translating it and describing it. With pratice new information sets work better, and can become translated easier.
This entire post is actually an example of this. I intuitively understood all of this in my head, but it takes time, trial/error, and a lot of effort to get it down. This is also why I started by saying "it's hard to explain". In a way it is ironic to say that it is hard to think about how I think and then further explain it.
*this post was a stream of consciousss. Which was (in hindsight) done on purpose to retain accuracy and authenticity of this.
ETA: I failed to answer the last two questions, sorry.