These days I'm round than the wheel--so that's not doing much for me! But otherwise, yes, I leave the jack und the car, with the jackstand, can't hurt to have two. However I often use wood cribbing, if it's good enough for ships, it's good enough for me.Totally agree with sliding the wheel I've removed under the vehicle I'm working on, it also keeps it from being a tripping hazard.
I also make sure to lower the car onto the jack stand while keeping some contact pressure on the jack. Belts and braces!
And as mentioned earlier, they might not be frame rails, but whatever those are, that is my jack and jackstand point(s). Using cribbing at least spreads out the weight.