Yes. POT file is provided as a base for translation in the root folder for each plugin. Translation files should go into languages directory, and WordPress must be set to your language to load the file. File name for translated and compiled MO file must be the same as POT file with addition of language code: {plugin-name}-{language-code}.mo.
Yes. Each site in the network can activate and use the plugin.
This can happen if you have some cache plugins active. You need to recheck all plugins settings, save them to make sure all are applied. Than clear out cache (if you use cache plugins).