1) You can create templates at a space level, if you are a space admin there, and global ones in global admin -> templates
2) You can't do this. A template is only used at the time of creation of a page, and the pages do not retain any record of the template used, because it doesn't matter.
You probably do not really want to do this anyway. If you did, then you would be enabling a system that could destroy a whole load of stuff people don't want you to. Imagine my work - we write proposals, service agreements, statements of work and so on, all from templates. Some of them are part of contracts. If you changed the template, you would be changing something that's in a contract. You would need to implement a system that checked with every owner of every document created with it to check if changes are ok with them, and you'd quickly end up with everyone saying "no" every time.
However, as you are asking, I suspect you genuinely have content that you do need to globally update. Instead of changing the template itself, I would change the templates so that they contain "include" statements and other ways of drawing in shared data. You keep that data somewhere central and update that instead.
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