Are there any kinds of relationship betweeen conservative and non-conservative forces with internal and external forces? If yes,please explain in detail.
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Yes. An external force is a non-conservative force, and a conservative force is an internal force. An external force will increase/decrease the energy of a system, so it's a non-conservative force. A conservative force does not change the overall mechanical energy, only changing it's form from kinetic to potential, so it's internal.
Note, that what I said does not go the other way around: internal forces are not necessarily conservative, as well as non-conservative forces are not necessarily external. For example, friction is non-conservative and can be internal.
