How tall are you? I'm 5ft 2 and found the handles were too low for my liking. You can't push it one-handed, but it does meet 1 & 3 of your criteria. Not sure about over grass though as I only used mine to walk to toddlers and back (10 min walk) and a quick walk around the town. I imagine it would be the same as pushing any other buggy with tiny wheels over grass, quite hard-going unless it's just been cut!
you want a baby jogger city mini. My friend has one and now its on my buggy wish list, suitable from birth, relatively lightweight (same as my pliko) but much smoother to push and fold with fab sunshade like pliko p3. Also one handed steering, so fab whilst holding toddler's hand, now if only it came with a carry cot it would tick all my boxes!
I would vote for a petit star. I think they are fab. Light to push, easy to fold, easy to go up and down kerbs. ? maybe not so good on grass perhaps but generally a great pushchair. I love mine and it looks lovely too!