If you want to ensure that MATLAB creates ticks and tick labels at particular values, I would use a combination of the xticks or yticks functions along with potentially the xticklabels or yticklabels functions.
figure
x = 1:10;
plot(x, x.^2, 'o-')
grid on
Note that the tick locations were automatically selected by MATLAB and the tick labels automatically generated. The grid lines do not necessarily correspond with the y coordinates of the markers. To specify locations on the Y axis, call yticks.
figure
x = 1:10;
plot(x, x.^2, 'o-')
yticks(x.^2)
grid on
Here the grid lines from the y axis do correspond to the markers.
If you want to add tick locations, calling union to merge the existing tick locations with the specified ones may be useful.
figure
x = 1:10;
plot(x, x.^2, 'o-')
automaticLocations = yticks;
automaticPlusSpecified = union(automaticLocations, x.^2);
yticks(automaticPlusSpecified)
grid on
Though this is a bit messy since 0 and 1, 9 and 10, 49 and 50, and 80 and 81 are so close to one another. The multiples of 10 are from automaticLocations while the others come from x.^2.
As for your other question about yline, the label used to display the line is different from the display name used by legend. You can set both, though. In the example below 7^2 is the label displayed near the line while 'Seven squared' is the DisplayName property value that legend uses.
figure
plot(x, x.^2, 'o-')
yline(49, 'r:', '7^2', 'DisplayName', 'Seven squared')
legend show
If you want to control which objects appear in the legend, assign the handles returned by plot, yline, or other graphics commands into a variable or variables then pass a vector of those handles whose objects you want to appear in the legend into the legend function.
figure
hPlot = plot(x, x.^2, 'o-', 'DisplayName', 'x^2');
hYline = yline(49, 'r:', '7^2', 'DisplayName', 'Seven squared');
legend(hYline) % Show just the yline in the legend
