1 Your husband does not automatically qualify to become NRI since you are an NRI. He becomes a NRI based upon the number of days stayed in India and /or outside India. The test of residency is dependant upon the number of days stayed in India during the current financial year and previous financial years and further on the nature of income earned also. Even if he is a Resident he may be Resident but not ordinarily resident also. His tax liability will depend upon his residential status.
2 A resident holding a bank account outside India is subject to compliance with the RBI regulations.
He can transfer money to you to your account in Dubai under LRS as per RBI regulations for your family maintenance and savings.
3 If you are investing in stock markets on your own from your own savings from the funds remitted by your husband within reasonable limits, normally there should not be any issue. However, if the funds remitted by your husband are used substanilly for investment in securities, then it is advisable to give the purpose code as capital transactions for investment. This is to avoid any issues in FEMA.
You need not return your savings to your husband and you may retain them for your own personal or investment purposes, as long as the investments out of the savings are within the reasonable limits. Though there is no specific limit, probably an investment upto 10% of funds transferred by you should not be an issue.