Income Tax: Get tax exemption of Rs 10,000 on savings bank account interest income

Q1. I have salary income, interest from saving bank account and dividends from equity funds. For interest from bank accounts, do I have to submit proof to claim deduction under Section 80TTA? Do I need to include dividends as part of other income?

You need to include interest from saving bank account under income from other sources. You would be eligible to claim deduction of Rs 10,000 under Section 80TTA. You don’t need to submit any proofs for it. Similarly, the dividend income would also form part of income from other sources but shall be exempt if total dividend doesn’t exceed Rs 10 lakh during a financial year.
Q2. My wife sold her flat in March 2018 for Rs 1 crore and bought a flat for Rs 1.5 crore in April 2018. Since sale and purchase fall in two different financial years, how can she show in ITR the sale amount which is offset against her purchase? She also wants to claim as refund the TDS on the sale. 
Under Section 54, if a long term capital asset is sold, the resultant gain can be invested in another house property within one year before or two years after, or within three years if the house is constructed; for claiming LTCG exemption. Assuming that the house sold by your wife is a long term capital asset, the gains shall be exempt from tax as the new house is acquired within the specified time limits irrespective of change in financial year.