Welcome to FT! From what I've heard, the best way to search for Star Alliance flights is on the Air Nippon (ANA) website. However, you'll need to sign up for their mileage program to search. I haven't actually used this yet myself.
Continental is pretty good as well, but it looks like you're not finding anything there.
Someone else will know if Continental or United has a similar redemption option.
Yes, since it's now past June 15th, Continental should allow you to book a one way award for half the miles. If you can't do it online, you can give them a call. United already offers this option.