Head income

ITR 3 will be applicable.

Coaching is service and should be declare under PGBP. No need to declare it as trader.

Shares trading be short term or intraday can be declared under PGBP.

While LT/ST shares investment gains should be declared under Capital Gains, including sched. 112A, if needed.

As such both the businesses are different and financial statements should be separate. Finally they will merge in income head PGBP.

Yes, You are correct.

You are welcome.                 

In such case the income from intraday is calculated separately, or is given in statements of the broking firm, so that is directly credited to capital acc, while business income is accounted in usual manner.