Samsung Galaxy 2 (Jelly Bean 4.1.2) In the stock "Phone" app, on the "Keypad" tab, how can you enter a "space" character?
It's not specifically the Phone app. You can't enter a space into any field where the app has said it's expecting you to type a phone number.

On the Samsung dialer, you can use a * to match a space in a contact's name e.g. 6453*56637 to match Mike Jones. I don't have an S2 to check this on, but that's how the dialer on the S3 works, and I'd expect they're both the same.