Background:
Disposal of investment on closure of a fund would amount to "transfer" under the Income Tax Act and the loss incurred on such transfer would be "capital loss". "Capital loss" can be set off only against "capital gains", which may be in relation to a capital asset situated in India or outside India. For a resident, a capital asset, whether situated in India or outside India, is on the same footing.
The capital loss incurred by you would be short term or long term depending upon the period of holding of the investment. The period of holding to be seen is different for different categories of assets. Thus, it would depend upon the type of your investment (whether it is in the form of shares, units in a trust etc.)
"Short term capital loss" can be carried forward/set off against both short term and long term capital gain. "Long term capital loss" can be set off only against long term capital gains. Further, such losses can be carried forward only upto a period of 8 years succeeding the year in which the loss is incurred.
As far as other income (in the form of dividend or other distribution, as the case may be) is concerned, such income would be taxable as income from other sources (tax rate will be as per applicable slab rate).
Answer to Query 1: Further information is required regarding nature of the investment fund, period of investment, category of income etc. to ascertain the exact tax treatment.
Answer to Query 2: Yes.Capital loss in relation to a foreign asset can be set off against capital gain generated in India (or outside India), as per the legal position explained supra.
Answer to Query 3: Yes. Carried forward capital loss can be set off against such capital gains as per the aforementioned provisions.