Lots of questions here, I'll see how many I can address. To be clear, $K_L$ and $K_U$ **are summaries of our current knowledge**. There is some true kissing number in each dimension, and hopefully we'll learn what it is someday; this is just what we know now.

(1) The $n$-dimensional kissing number, $K$, is defined to be the maximum number of non-overlapping spheres capable of touching an $S^{n-1}$. So saying that $K_L \leq K$ means that we have found a way to place $K_L$ many non-overlapping spheres so that they touch an $S^{n-1}$. Of course, we could place fewer spheres in contact with a sphere (as you say, we could place $0$), but $K_L$ is the largest number of spheres we have managed to place.

(2) Probably not. The conjectured best packings in $9$ and $10$ dimensions are the $9$ and $10$ dimensional laminated lattices, with kissing numbers $272$ and $336$ (see here) and the conjectured best lattice in $12$ dimensions is the Coxeter-Todd lattice with kissing number $756$; these are less than the numbers in your table. I see no reason that the densest packing should also have the highest kissing number, but since we have very little understanding of either problem, I don't know if we can rule it out.

(3), (4) and (5): The dimensions $1$, $2$, $8$ and $24$ are very special, because we know exactly what the densest lattice is and it also achieves the maximum kissing number. In dimension $3$, the Kepler conjecture, now proved by Hales, establishes that the optimal density is achieved by the face centered cubic lattice, which indeed has kissing number $12$. I don't know what is going on in dimension $4$.

Again, what is going on here is that there is special structure which allows us to know $K$ exactly in these cases, and so $K_L = K_U$. The other cases where $K_L < K_U$ in the table, reflect our current ignorance, not eternal mathematical truth.