No Lift 360 Swap Tips/Suggestions

If your engine hoist is that sketchy, then I have to agree with the Professor, toss it before it kills or maims you.
As for your other questions, the transmission will be fine if you put a floor jack under it for support, but use a scrap piece of 2x4 or 2x6 between the jack and the transmission pan to prevent damage.
You can jack the car up using the k member, then place good quality jackstands under the frame rails to support the car. Make sure you leave enough clearance to lift the engine out of the car without contacting the ceiling of your garage, I prefer to keep the chain as short as possible.
Personally I don't use ramps because they take too much space, you will have to get underneath the car at some point in the process of the swap.
Engine levelers are valuable, but not essential to have, I have used them on occasion, but I don't own one and have successfully done dozens of engine removal and installation jobs.
Ask any questions you may have before you attempt this as you haven't done or seen this done before.
The headers shouldn't be too hard to install after the engine is in, and you will find the extra room to work without them attached to your benefit.