I have to set my seat very high, the maximum height possible. As a result, not only my knee would be almost straight when the pedal is at the lowest point,
That's standard practice in fitting a bike.
but also my feet is very far from the ground when letting my leg straight down from the seat (i.e. my feet could never touch the ground even when the bike is slightly leaned to one side when stopping at a red light: I have to get off the bike completely).
The usual technique is to slide forward off the saddle so your feet reach the ground while straddling the top tube. When you resume riding, you stand on the pedal to lift yourself back into the saddle.
And I remember I had hip pains when saddle was set too high and the ride demanded some effort.
So in short, either my seat is too high causing hip pain, or it's too low harming the knees. The point is there is no point where the seat height can accommodate both for me.
Shorter crank arms produce less range of motion in the leg joints and may help.
What's the problem? Is it my leg proportion unsual (thigh/calf too long/short), or the crank arm is too long for me (which may mean the bike is too big for me?)? Otherwise I feel perfectly comfortable with my bike.
From your description, I wouldn't think the bike is too big for you, but perhaps the cranks are too long. If you have arthritis or other joint problems, shorter arms may help. Otherwise, if your expectation is that you should be able to plant your feet on the ground while seated in the saddle, one of the "crank forward" designs like the Electra "Townie" may need your requirements:
