I am a non-resident alien transferring a limited amount ( in dollars post tax) to India every couple of months.
Assuming you are transferring this into an NRE account in India or atleast NRO account in India. As a NRI, by regulations one should not hold normal Savings account. This has to be converted into NRO.
I put that money as a fixed deposit in a bank (which gives 6-7 percent annual return)
Assuming you have FCNR deposits. Also assuming that you are declaring the taxes in your US Tax returns and paying tax accordingly. There is no tax in India on FCNR. If this was in ordinary FD or in NRO account, you are declaring and paying taxes in India as well as in US.
What is the max limit on transferring money back from India to USA?
If you have transferred this into NRE account, there is no limit. Other account there is a limit. Read more at Liberalized Remittance Scheme and here.
What are the legitimate ways to transfer the money?
From India point of view, this has to be Bank to Bank transfers. You can't carry cash [Indian Rupees] outside of India beyond Rs 25000 [or 15000?]. You can't hold excess of USD 250 without valid purpose. Western Union is not authorized to transfer funds out of India.
Will there be any tax levied?
No assuming you are already paying taxes on the Interest in US and depending on the type of account in India.