"she won't ever allow a new R with me to work so give up"
I know exactly how you feel as many others here do. The truth is very few of our relationships will work out. Living with hope and trying to detach has been impossible for me. Its taken a year, but most of my hope is gone. I finally admitt the reality that it will never work out, mainly as you say "because she refuses to consider the possibility". Its took about a year for that to sink in.
I think as long as you are not doing things to intentionally hurt her, they are OK. For example boxing up their stuff. I'm ready to do the same, because I'm tired of looking at the stuff thinking "she left some stuff here, maybe that means she is coming back". I'm so tired of living in that dream world.
If you want to date for the right reasons then date. I want to date because I want to share my life with someone, but I know I'm not ready, so I dont. I would never date just to make her jealous. She started dating, because she cannot stand to be alone (not a very good reason in my opinion). This is really up to you, you just have to ask yourself why you want to date.
My ex actually gave me the garage door opener. I never had one, so I actually forgot about it. She also gave me the key to the house. I never asked for it, I guess she felt she no longer needed it. Does your x need the opener, if not you should ask for it back.
I dont believe in giving up, but I also dont believe in beating a dead horse. I like to think of it as not giving up, but accepting what life has delt me.