The first thing to get clear is that the idea of 'permanent' and 'continuous' or 'temporary' are ways to express quite a tricky idea. Almost any such words give at best a rough idea what is going on.
Suppose we divide verbs into those that describe actions or events (I walk, I drive, I eat....), and those that refer to states of affairs (! know, I like, it hurts...
The distinction between so called 'more permanent' and so-called 'more temporary' seems at first sight obvious, especially because of the cautious qualification in the use of the comparative 'more'. But the easiest way of looking at it is to say that the the continuous present is referring to an event or action that is taking place at the time at which the sentence is uttered.
1.1 She is driving to Newcastle
1.2. My company is conducting a review into its internal efficiency
1.3 The level of the Thames is rising at such an alarming rate that within house it may break its banks and flood the streets.
We are talking about events that are physically taking place now. But they are not 'temporary' or 'more temporary', so much as references to things actually taking place at the time of writing or speaking. That is the function of the 'present continuous' in relation to verbs of this sort. So from your question it is clear that you know the difference between 'I play the flute' and 'I a playing the flute. In French, of course, 'Je joue de la flute' can only be made fully univocal by reliance either on context or on phrases like 'Je suis en train de jouer de la flute.' ('I am in the process of playing the flute').
So the so-called 'simple' present refers to what is the case in another sense: stable states of affairs over some sort of long term. These are works that refer to states of mind or body or about the way things are: words such as ''! work in the factory down the road', or 'I agree with you', or 'the tide rises and falls at regular intervals under the influence of the Moon.'
The problem is that states of mind notoriously blur the boundary between the two kinds of present.
2.1 I know the square root of sixteen. I suppose I might forget this piece of information at some time. But to all intents and purposes, this kind of state is perpetual. It is not something I am doing now. Moreover, we recognise 'I am knowing the square root of sixteen' as a sign that the person saying that is not a native speaker of English. Moreover, this kind of knowledge is not something I am aware of all the time that I know it. It it not a conscious presence to me. I do not walk around thinking about it.
However, there are some such situations, where speakers seem to feel as if they are in the middle of the grey area.
2.2 Do we say "I suffer from a chronic illness.", or "I AM SUFFERING from a chronic illness."? Well, we seem to feel pulled in both directions. The rule doesn't help us. The chronic illness is an established and continuing state, so perhaps the simple present should be used, but a chronic illness is surely a something that is happening to me and so perhaps the continuous present should be used. There is no answer.
And then there are your example of apparent exceptions.
2.3 She lives or is living with her parents. You could draw some distinctions here. With the simple present, it does sound (to me, subjectively, as if this means that this circumstance is certainly long term. With the continuous present it looks more like a temporary arrangement, while she completes a PhD, or is getting her life back together after splitting with a partner. But we are in the grey area.
2.4 I like or am liking my new car. Here I should say that the use of the continuous present is a fairly recent and special usage. It is more like saying "I am enjoying or relishing my new car". It is, in fact, something I am experiencing it at least until I am fully ised to this magnificent automobile. But this will fade with custom, even though I shall not like it any the less - till it gets old and starts needing costly repairs or is displaced in my mind by a newer and more desirable model.
2.5 I'm missing (or I miss) you. This is, I think, bang in the middle of the dilemma. I can miss someone in either of these two ways. Because Missing someone, though not, perhaps, felt literally constantly, is felt often enough in a day to count as something that is happening to me. And yet it can equally be seen as a steady state, part, if you will, of my settled feelings about the person. So continuous and simple presents are equally possible.