Question: Is it possible to grow tomatoes as a pot plant? In the limited space I have I can afford pot of maximum depth = 12 cm and diameter = 12 cm. what size pot will be ideal to start with?

In India what would be the best time to plant them and how can I take care of it at later stages?

Sun is not that harsh is winters here - temperature ranges 5-35 degree centigrade, average day temperature would about 24 degree centigrade.

Plant will be placed outdoors and will get all sunlight all through the day.

Answer: 
I know you've said you only have space for a 12" pot, but if you can find any way to accommodate a larger one, you've got a better chance of success. 30 centimeters would be closer to the size recommended for container-grown tomatoes. I've personally had some success with a 20 centimeter pot. Anything you can do to get closer to that 30 centimeter mark is going to give you a better chance of success.

When you buy your tomato plants or seeds, look for a dwarf variety. If you want the plant to look compact (more like a decorative plant), you should look for a dwarf *determinate* variety. If you don't mind a sprawling, viney plant that needs to be trellised, you can consider a dwarf *indeterminate* variety. This might work, for example, if this outdoor space is a balcony, and you could afix the tomato plant to the balcony railing as it grows. 

Here in the US, many of the common dwarf determinate plants have names with the word 'patio' or 'balcony' right in them (Patio Dwarf, Patio Princess, Balcony, etc.). Stupice is another that is frequently recommended for pots. Sweet Baby Girl is a dwarf indeterminate cherry tomato that is also easy to find here. I'm not sure which, if any, of these are available where you live, but you should be able to find that information locally.
One of my best tomato seasons was when I was living in an apartment with a balcony that got sun about 4 hours a day. I grew 6 plants: 3 in each of two 18" pots. They were some variety of "patio tomatoes". That was in 1989. I didn't match the dozen dozen tomatoes I got that year until last year in my 4'X4' planting bed. However, this year a had one cucumber plant that yielded 100 cucumbers.