It is not that meditating disables anything; rather, meditation consists in observing consciousness in a way that is orthogonal to these things. When meditating, sometimes (often!) you are remembering things, but sometimes you aren't. And in fact what you come to realize is that this is also true in daily life: there are many, many gaps during the day when you are not remembering or thinking about anything. According to your question, wouldn't you just immediately forget what you are doing and stop in the middle of your day? Well, no, you don't, and you can hypothesize as to why (unconscious processes or whatever) but the point is that unconscious processes can be explained without hypothesizing consciousness (isn't that like what a robot has?)

All I can say is, try meditating sometime and you will see. (I don't recommend mantra meditation, but rather something more like Vipassana or "mindfulness" or any meditation that is not about distracting your mind by keeping it busy).

When you become comfortable with meditation, you become very aware of what your consciousness is doing. You gain a palpable sense for the present moment. Once you have that, it makes a lot of these kinds of questions unnecessary (or at least the questions become very different in nature). If you don't have this taste for the present, then asking/answering questions like this is like trying to explain colors to a blind person. It just doesn't work because most of the questions are about things that don't really have anything to do with consciousness.