Can I subscribe to questions and is there a way to filter those subscriptions (for example, by tag or a search filter or something)?
You can subscribe to tags, hover over any tag you want to subscribe to and you will see details about the tag and options for
subscribe - thats how I subscribed to the daily Joomla Questions on SO.
You can subscribe to tagged searches. I get daily emails from Stack Exchange on questions matching "joomla".
To set it up, go to https://stackexchange.com/filters and log in. From there, you can set up a filter that emails you a daily summary of questions and links to them for answering. Pretty useful.