Parameters of two port networks

Only a network made up only of ideal resistors will have its network parameters constant.

For linear networks containing capacitors and inductors, the network parameters vary with frequency.

For networks with nonlinear elements like diodes or transistors, the network parameters will also vary with applied bias. Furthermore the network parameters won't fully characterize the circuit behavior if the input amplitudes are not "small".

Why for these parameters, there is a special mention ... of reciprocity condition in each parameters? , are reciprocal networks have some special relation with these parameters other than just a mathematical relation?

A reciprocal network is in some sense a reversible one. It works the same way whether you treat port 1 as input and port 2 as output, or vice versa. For example, a coaxial cable ought to behave as a reciprocal network.

It's useful to know the properties of the network parameters of a reciprocal network, for example to be able to check quickly if the parameters you measured (or someone shared with you) are faulty in some way. For example, if you measure a coaxial cable and don't get $S_{21}=S_{12}$, then you made a mistake in your measurement somewhere.

If the reciprocity conditions give some symmetry in the parameter matrix it can also save you calculation effort. If you're analyzing a reciprocal network and you calculated $S_{21}$ you can just plug the same number in for $S_{12}$ rather than doing more calculations.