Problem - score attached

2/2 time means 2 half note time means the same look as 4/4 time, but the beat is every half note.

Yes, as I explained in your other thread, this is absolutely correct. If it helps, here is a site that explains time signatures reasonably well, and demonstrates how 2/2 works and why what you posted is *correct* notation:

http://www.learnmusicfree.com/lesson/fundamentals/time_signatures.html

As you can see, if you want only two crotchets (aka quartet notes) in a measure, you need 2/4, not 2/2.