In the first question, if 'FATHER' was replaced with 'SPOUSE', then clubbing provisions u/s 64 will come into play and the Income on deposit of gift amount will be clubbed in the hands of Individual and such individual will have to pay the tax.
However, it is also notable that "Income on Income is not to be clubbed". For instance, if the spouse were to invest the Income on gift (Rs.10,000 in your case) and the spouse earns another Rs. 1000 on such deposit. Then such income on income ie., Rs. 1000 is not to be clubbed.
Regarding the last query, Gift is something for which no deduction is available under any heads of income. Ultimately, the donor of gift ends up paying tax on gift since he/she does not get deduction for the same. Hence you are right to say that Gifts have no tax deductions under the Income Tax ACt, 1961.
In some instances, the recipients are exempted from tax. eg. Relatives, Gift at time of marriage, etc.
(But donors of gift are not eligible for any deduction unless its given by a business concern and the purpose is Sales/ Service Promotion)