I have established an LLC in 2018. have not done any business. Can i open an account at a stock broker so that i can buy & sell stocks

yes the LLC can open an account subject to the rules and regulations of the broker. This might require you to get an EIN for the LLC, if you don't have one, and the broker won't allow use of your SSN. As a single member LLC that has not elected corporation taxation, the activity would be reported directly on your 1040. Alternatives would include electing C-corp or S-corp tax status, but they would probably not be efficient from an income tax standpoint. Either would require filing a corporate return 1120 or 1120S. A C-corp would involve double taxation since it would pay taxes on its income and any profit you took out would be subject to various rules as to personal taxation. As an S-corp, its activity would pass through to your 1040 as if it didn't exist. Limited liability protection is not perfect. State laws vary.