I want to add a water filter to the household system. I was thinking a single stage carbon or similar. Should I add it after the pump or before. I was thinking after.. would it damage the pump and would there be much pressure drop?

A total reverse osmosis is better.

If you only want clean water, not drinking water, then a deep bed sand filter with active filter media or one of those stainless steel ones which have various types of filter media. Drinking water can be made with a countertop or under the sink filtration unit.

i have a steel tank type one that i brought at home pro 10 years ago, (8,000 baht or so) uses charcoal and sand, works fine for showers and washing but still but the 20 lt bottles for drinking

I use a pump cause i have a 2 story house and it connects from well to pump to filter to the house