Dear Mr. Sandeep,
With respect to your quarries please find below answers :
a) There is no limit on personal investment outside India, except AD Code Bank approval which is required every time you do the transaction. Unless the transaction is of purchase of property in other country.
b) Since the investment is situated outside India, we need to check DTAA provisions on the said transaction value based on the name of country where investment is made. But mostly any transactions done in the shares and mututal fund are taxed in the country of transaction only and not in the country of residence except in case of person of U. S. Resident.
c) In case of encashing the fund and and repatriation to india said transaction shall not be subject to any tax. However if this funds brought to india and kept in NRO Account than same can not be invested again in any foreign asset in the future and if it is kept in NRE Account than same can be invested again in foreign asset. So there will be no as such tax effect on the transaction referred by you.