As per Proviso to Sec 24., which states as :-
Provided also that no deduction shall be made under the second proviso unless the assessee furnishes a certificate, from the person to whom any interest is payable on the capital borrowed, specifying the amount of interest payable by the assessee for the purpose of such acquisition or construction of the property, or, conversion of the whole or any part of the capital borrowed which remains to be repaid as a new loan.
Explanation.For the purposes of this proviso, the expression new loan means the whole or any part of a loan taken by the assessee subsequent to the capital borrowed, for the purpose of repayment of such capital.
Thus, it is nowhere mentioned that you can not claim Interest paid to Personal Loan under Sec.24, It is up to the assessee to prove that the personal loan was used for construction of the house. You have to keep the following ready
01. Certificate of interest on Loan
02.Proof of construction, such as bills used for purchase of materials for construction.
All this is not necessary if you take a housing loan from a bank, It becomes the duty of the Bank to ensure that the funds released is used for construction and ITO will admit a certificate for intrest the final proof.
For the second part of your question, When deducting tax, your employer acts as the agent of Govt and has the Power and responsibilities of ITO.