Someboby please help me with understanding of the following question. I have many postgreSQL databases with osm data on a server. Each of them contains the map of the certain country. I want to look through the maps on my notebook via offline WMS client. Can I convert databases to .mbtiles for tileserver or is there another way for a best perfomance?
Let us start from the basics. Your postgis database contains the vectors that make up your features.
Mbtiles is a special format which stores tiles that make up a map. It is a representation of the data rather than the data itself.
You need some way of converting from the data to this rendered tileset in Mbtiles format.
To do this you need a software like say tilemill which is used to design maps and create rendered tiles.
There is nothing wrong with @Devdatta Tengshe idea but then you'd have to go through a format conversion. You can run postgreSQl without a full installation. I've used that before. You can export your Postgres database and import it on you laptop. What I like about the running without install idea, is that if you don't want your Postgres service running, then just don't start the batch file/shell script.
Why not just view them with a GIS? QGIS can, obviously, read direct from PostGIS.
If you render them as tiles, you certainly can view them on your laptop, but you can't get more info that what you have used to style the layers.
Perhaps you should rephrase your question, and state what you're trying to achieve, without proposing half a solution too!