Hi,
As your primary reference for this question, use: **broken link removed**
Decomposing your multipart question into its components, and treating each one with reference to sections in the above paper, we have:
1) what effects will the primary inductance of a non-ideal transformer....
Refer to section 2.15. This shows what you need to do, in order to convert the ideal transformer model into the non-ideal.
2) what effects will the primary inductance of a non-ideal transformer have when the secondary is shorted and also when opened ?
Refer to section 2.14. This explains secondary to primary impedance transformation. Apply those explanations to your two situations. In addition to this, you will need to consider the effect of the most important non-ideality, given in the top paragraph on page 21. Formulas are in the appropriate sections of that paper.
3) And also what effects the secondary inductance will have when the primary is shorted and also opened?
The primary should not be shorted (by which I understand that a wire is connected between the ends of the primary winding). Why would this be so ?
If the primary is open-circuited (by which I understand that only one end of the primary winding is connected to the AC source), how much current would be passing into the primary winding ?