Use low temperature 138°C bismuth based solder, you can get it in wire or paste for reflow.
This has many advantages, for the reflow, you can use a much lower heat curve, which is more forgiving, especially if you have plastic connectors.
Small "hobby" reflow oven often have uneven & unprecise temperature and using low temperature solder will give you way more headroom.
Another advantage, is that for prototyping, it will be much easier to replace components, rework and tweak things around.
Apply the paste with the stencil in one swipe, especially with tight count components, this will reduce bridging.
You will always have bridging in tight pitch component. Use solder flux and cupper wick, coat the wick with the solder flux and use that to remove bridging.
Avoid component with pads underneath, like BGA, because you will never know if they are properly soldered without an X-Ray machine.
Stay with minimum 0603 component size unless you are really size constraint.
As for the shaking, steady the side of your palm on the table and work with the tweezers and your fingers.
You don't need to place them very accurately, you can always, once placed & before reflow, go under the microscope and push them around with the tweezers until they are properly placed.