1. There is no such limits for investments to be made in foreign stocks.

2. Yes you can still do the trading.

3 . The SEBI or RBI do not put any restrictions . 

You will be though liable to pay Income Tax at the prevailing rate in India. 

1) If you're not going to invest directly from Indian account to Foreign Account, then you can buy/sell in the foreign account. (But if there are any changes in your account from India to US) then rule gets changes. See below.

2) Yes, Please see below.

All new amendments are applicable from 1st April 2020.

Taxation in Indian for RNOR (Resident and Not Ordinarily Resident) :

• Income received or deemed to be received in India
• Income which accrues or arises or is deemed to accrue or arise in India
• Income which accrues or arises outside India from Business controlled in India or profession set up in Inida or other Income.

1. As per RBI. this limit is USD 250,000 for resident Indian , otherwise there is no limit in your case. 

2. Since, you already returned Indian , hence your foreign account cannot continue as per section 13 of the FEMA . and further you cannot buy/sell stocks in foreign account.

3. Yes

Dear Sir,

There are certain restrictions of such investments as mentioned by you. So, you are suggested to contact the concerned department of the company as also the Indian Consulate in this regard to find the more details, procedures and processes involved. 

There is no limit in investment of fofs in foreign countries but when it comes for real estate and direct income, shares etc is $250000 per financial year you can remit through liberalised remittance scheme

Your United state investments will be intact and there is no limit however you will have to declare in your income tax return the investment you have and any income from those investment that has to be text in US to your income tax return to avoid double taxation India and United States have double taxation avoidance treaty so that you can take credit of any tax paid in United state in your Indian income tax return

There are two ways to invest in US stocks, either you have a brokerage account and invest in US stocks or invest in US focused International mutual funds in India e.g. ICICI, Franklin, etc. RBI allows investment of residents through both routes.

1. For investing through brokerage firms, you are allowed to invest under the LRS (Liberalized Remittance Scheme) i.e. upto $250,000 per year per person. For direct investments in US equities, there are certain brokerage firms that do offer investment in US. 
2. For investments in US focused mutual funds in India, there is no limit for India residents as investments are made in India. You can invest in International mutual funds or International Fund of Funds and invest in INR in India only.

1. No, in this case there would be no limit. 

2. Yes.

3. No.

1. Since you have not invested through Indian account,  the question of limitations do not arise.  Investment through LRS  shall be restricted to USD 2,50,000.

2. You can continue the trading activity in India also.

3.  Except for the levy of income tax, there may not be any other restrictions. 

1. No limit..

2.You can buy/sell stocks. 

3.income from foreign investments would generally be liable to tax in India. In case of non residents, such income is not liable to tax as long as it is not directly received in India.

1. No there is no limit on investment of money outside India Till you pay income tax on profits earned from trading. 

2. Yes you can still trade in foriegn account.

3. No residential status diesnt have impact on buying and selling of foriegn shares.  

It is better for you to consult a practising Chartered Accountant, as these queries relate more to financial matters than legal. You may please read the relevant circulars and notifications on the RBI's website on these topics.