Can Australian 3DS games work on an Indian 3DS?
They should, yes. They are both what Nintendo classes as the PAL region.
However, many 3DS consoles sold in India turn out to be imported from the USA and would only work with US/CAN games.
Does Nintendo 3DS work with Pokemon games Like Pokemon Black and white version or future PKMN games?
the games might not match your 3DS region. all the 3DS games have region lock, it means that if you have an American 3DS only NTSC=american games will work on that 3DS and PAL=european or NTSC-J=japanese games will not work, same for the European and Japanese 3DS If it is not reading any games, then that points towards the 3DS' card reader being broken, you'll need to have it repaired.
No the 3DS game cards are shaped slightly different then the Nintendo Ds. Of course if you could put the 3DS game cards in the Ds lite it would still not work because the features and intense graphics the nintendo 3DS requires for games can't be used on the Ds lite. Don't buy 3DS games for the Ds lite as it just won't work. You can consider buying a 3DS however as the 3DS is…