Answer for Q1: In case the transaction is done through a recognized stock exchange for which the security transaction tax is paid, you are exempted from the long term capital gain tax under section 10(38). The bill issued by your share broker will have details whether the security transaction tax has been paid or not.
In case you are trading frequently on the stock exchange generating bulk of your income by buying and selling stocks, income earned from stocks is considered as business income. In such a scenario the income you earn from sale of stocks gets added to your business income. Of course you can offset the income by showing expenses for internet, stock market advisory etc to reduce your overall income tax liability.
Answer for Q2: Short term capital gain is levied on equity stocks that you buy and sell within one year. The taxation depends on whether you take the delivery of the stock in your demat account before selling.
For trading through a recognized stock exchange, you will be levied 15% short term capital gains tax. However the short term capital gain tax is applicable only in case you have taken physical delivery of the stock in your demat account. For example if you are a day trader and buy and sell equity stocks for active trading without taking delivery of the stock in your demat account, the gains made are added to your income from other sources. The income tax rate depends on your final tax bracket depending on your overall income. The tax in such a scenario may well exceed the short term capital gains tax bracket of 15%. The good news however is that you can offset trading charges with your business related expenses.
In your case since you have an annual income of Rs. 3 Lakhs and a short term capital gain of 50,000. Assuming you took physical delivery of the stocks before selling them you would be charged 15% for all short term capital gains as tax. So you pay 15% of 50,000 as short term capital gains tax and 10% of 50,000 from your salary (Rs.3 Lakhs minus the exemption limit of Rs. 2.5 Lakhs) at 10%.