Let's say we have a population of size $N$.How many chromosomes should we select using any selection method and what's the point if the population size is fixed ?
There's not a generally correct solution to this.
In practice, students experimenting with this for the first time might pick values $\in\left[0.1,~0.25\right]N$, mostly because:
This retains a significant amount of diversity.
This allows for each of the selected chromosomes to have $4$-to-$10$ offspring each, enabling the algorithm to mutate each chromosome in a bunch of different ways.
In principle, it'd tend to vary. In fact there's no reason for it to be constant.
Example: Say that all $N$ chromosomes do almost equally as-well despite having diverse genomes. Then, there'd be a stronger argument to maintain more of them (and perhaps grow the population).
Example: Say that only $3$ chromosomes were any good at all, while the rest did horribly. Then, the algorithm might do well to disregard all but the $3$ good ones.
let's say we use Proportionate Fitness selection method and we chose $k$ 'good' chromosomes, then only on those $k$ chromosomes we apply crossover and mutation and let the other unselected ones untouched to the next iteration ?
The "good" chromosomes have some effect on the next generation while the unselected ones tend to be discarded.
In general, the principle's that the good ones should have a stronger effect on the next generation. Beyond that, there's no general requirement for how things must be done.
A lot of this is really vague, which is what can make genetic algorithms a lot of fun to play with because there're all sorts of experimental schemes to try out!