Where it is possible to buy self-tests for malaria and Coartem in Trivandrum (Kerala)?
(Self-test is a piece of special paper where you put a drop of your blood to detect malaria infection by yourself without visiting hospital. Coartem is the most efficient medicament against malaria.)

Does the test tell you which of the four types of malaria it is so that treatment can be tailored to that type.?

I don't know. I have never seen such tests. And I would like to buy one just as additional protection measure (like condoms). Or at least just out of curiosity.
However, i think you can read about capabilities of such tests online.

Why? A doctor/lab will do this for Rs50..
I want to buy it for a period after returning back from tropics.
Where it is possible to buy self-tests for malaria and Coartem
The first thing to do is follow insect bite avoidance measures.
Wear clothing that covers as much of the body as possible such as long sleeved clothing and long trousers.
Apply insect repellant to exposed skin morning and evening. DEET is still the gold standard.
Mosquitoes may bite through thin clothing, so spray an insecticide or repellent on them; or have impregnated clothing.
Stay in air conditioned accommodation.
Use insect repellent plug-in diffusers in accommodation every night. Burning pyrethroid coils and heating insecticide impregnated tablets all help to control mosquitoes.
If sleeping in an unscreened room, or out of doors, a mosquito net (which should be impregnated with insecticide) is a sensible precaution. Nets that have pyrethroid incorporated into the material or bound to the material with resin have an expected life of 3-5 years and are superior to nets that require re-impregnation.
The second thing to do is seek professional diagnosis and treatment.
I want to buy it for a period after returning back from tropics.
See above. Seek profesional diagnosis and treatment.
If you have any symptoms on your return, or within a few months of your return, you need a post travel checkup.
This checkup should be undertaken by a doctor experienced in travel medicine as soon as possible. Tropical diseases and parasitic infestations are best treated early. Some can be fatal if left untreated.
For example, you need a post-travel checkup if you are suffering any of the following after a trip ( this list is not exhaustive).
Fevers: Fevers are particularly serious if you have visited a malarious country, even if you have been taking malaria pills. Malaria can develop years after your visit.
Persistent diarrhoea
Stomach pains
Dark coloured urine
Skin rashes or lumps
Persistent cough
Headaches
Joint pains
I got all those. Can I self diagnose myself as having malaria or is it just the ravages of time:). You will know its malaria if you get it:(. On the other hand I don't recall the symptoms. It was eight days of blank and my mother in law constantly trying to get me to eat usually unsuccessfully..

- As I found through reading articles online, Coartem is used solely for treatment. So, prescription and appropriate medical condition is required for purchasing even if it is available for sale.
- But Malarone (atovaquone+proguanil) is suitable for both prophylaxis and treatment. So, getting prescription is very easy in healthy condition. Malarone is not sold officially in India. Only its local generics are available. One of them is Yashirone and another is (probably) Paldrugone. And probably there is another one that is called exactly "atovaquone + progunanil", but I'm not sure.
- However, all generics are unavailable in best Trivandrum pharmacies/hospitals too.
Maybe only for online sale or in larger cities at North.

Clarification about rapid test kits. As I found they are used for detecting tropical malaria and practically it is enough. Because if it is not tropical malaria it is relatively safe (you will not die in 3-4 hrs), and medicines for non-tropical malaria are available around the world easily; it means, you may relax and go to any hospital for treatment. So, such test kit is useful for discovering potentially deadly situation.