Tumblr's social features can be a bit hard to figure out at first, connected as they are to your primary blog. For example, although you can receive asks and other types of messages on your side blogs, you can only send them from your primary blog. The only exceptions are replies to messages sent to a side blog, which will appear as if they were sent from the side blog.
Enabling the ask feature on a side blog works exactly the same as doing so on your main blog. Click the "Settings" icon on your dashboard, click the name of the blog for which you want to enable the feature and then enable the check box labeled "Let People Ask Questions." By default, the title of the ask page is "Ask Me Anything," although you can change this to anything you want; you can also enable anonymous asks, which are disabled by default. When you're done adjusting the settings to your liking, scroll to the bottom of the page and click "Save."
Checking Your Asks
Whenever anybody sends an ask to one of your blogs, Tumblr sends you an email notification by default, although you can disable that in the settings. To do so, click "Email" and disable the check box in the "New Messages" column for each blog for which you don't want to receive a notification. Asks, like all messages, appear in the inbox on your dashboard. You can tell whether they were sent to your primary blog or to a side blog by the header. Asks sent to your primary blog are labeled "username asked you," while asks sent to a side blog are labeled "username asked blogname."
If you answer an ask publicly, both it and your answer will appear on the blog to which the ask was sent. There is no direct way to post the ask to a different blog -- if you want to do that, you either need to first post it on the blog to which it was sent and then reblog it, or to take a screenshot of it and post that. Keep in mind that Tumblr doesn't notify the sender when you answer an ask publicly, even if she isn't anonymous, so you might want to tag the published ask with her username so she can find it.
When you answer an ask privately, the sender is always notified; you can only do this if the ask isn't anonymous, since Tumblr doesn't keep track of the usernames of anonymous senders. The answer appears in the Tumblr inbox of the person who sent you the ask; Tumblr also sends an email notification, unless the person disabled the feature. Regardless of whether the ask was sent to your primary blog or to a side one, the header for the response is always the same -- "yourblog answered you," with the username of the blog to which the ask was sent in the place of "yourblog."