John Fairbairn wrote:Does "endgame" always have to wait until the "middle game" in over?
No-one has answered this part of the OP's question, but it represents the real problem succinctly. The real problem is one of terminology, and even the Basic Endgame Theory page on SL manages to start off on entirely the wrong foot.
The first point is that it is more correct to talk about "boundary plays" (= yose) and these can occur even in the opening. They are common in the middle game. Conversely, the endgame can include plays (e.g. ko fights) that are not boundary plays.
The second point is that discussion of the topic is riddled with confusing usages of terms such as count, size, move, point, tally, etc. It is usually futile to start reading anything, even by an expert, about counting boundary plays unless you know for certain how these various terms are being used. It is not just that writer A may use one term and writer B another. It is that writer A may use the same term in two ways even in the same sentence. For example, with count you need to know whether the de-iri count or the miai count is being referred to. Context can help, but as the earlier posts in this thread show, it is unsafe to make assumptions about the context.
Even if you do come to terms, so to speak, with counting you need to remember that this is just one part of boundary play study. For instance, you need to be familiar with the many tesujis for this aspect of the game - not so very different from middle-game or life-and-death tesujis, but instead of good shape or life the goal is to gain extra points.
A further aspect of study is really for dan players, and that is thickness (i.e. solidity). Often you will want to play the most secure move rather than the one that looks biggest. This applies usually to boundary plays in the middle game (and ability here is one of the markers for very strong players), but it can occur quite late in the game, too, for example when there are still ko fights lurking.
There are also other kinds of boundary play strategy. One centres round the tedomari - getting the last move of a certain level. Just as in the opening where, say, there are three big 20-point big points you will usually try to improvise a plan to get two out of three of these, so with boundary plays: if there are three 2-point gote plays you will want to ensure you get two of them (this is often where thickness comes in). Timing is general is an important element of boundary play strategies.
Proverbs don't really cope with such a wide range of requirements, although sayings such "the monkey jump is worth 7 (or 8) points" are useful in various ways. I think the most unuseful advice is to stress the importance of sente. It is often plain wrong - usually the biggest move is best, often the thickest move is best, and often the tedomari is your goal. Sente is just a means. The end (or boundary

) matters more than the means.
When you see a pro described as "good at the endgame", remember that this should be "good at boundary plays". In fact it really means he is good at the middle game. It does not mean he is good at counting local positions - all pros can do that and they have very many standard counts stored in their heads. It means rather that he is good at evaluating boundary plays, potential as well as actual, at an early stage and so can make the right decisions as regards timing or thickness.