Do not panic. The issues you encounter are normal. Even the experts mess with such issues frequently..
All will work when you clean up the board's issues..
QFNs are easier to solder than the 0.5mm flatpacks or BGAs, imho.
You must apply a LOT of solder flux (the peach jam like stuff) otherwise you get shorts (the board must be over-flooded by the flux). The chip must swim in the flux when hot-air soldered.
I do not know whether your package has got thermal pad from the bottom, if yes then do NOT put a lot of tin on the thermal pad otherwise the pins will not reach the pads. Use a SMALL drop of tin there (like a 1mm diameter ball of tin).
Capacitors - large multi-layers ceramics capacitors may show "short" for a fraction of a second (as the capacitor is charging itself during the measurement) but after that you must measure >10MegaOhm. Better switch your multi-meter into Ohms and measure the resistance.
With QFNs, after they are soldered in, you may resolder the pins at the four edges with a thin solder tip and a LOT of flux. The chip will not desolder itself and you remove the shorts. Also I use a copper wick to remove shorts off the adjacent pins at the qfn's sides.
The markings on the package - you must to remove the flux with isopropyl or similar stuff. The markings are laser engraved into the epoxy package, when they are full of flux they disappear.
I always solder qfn or bga as the first device on the pcb, then I do measure with the ohmmeter resistance between the tracks (all reasonable combinations) to test such everything is ok.
When you read between the tracks:
~0 ohm - there is a short somewhere
~kiloohms - the tracks are connected to the chip
>10Mohm - no connection.
PS: when watching the photo of your pcb above - you use a lot of tin there (capacitors/resistors). 1/10th of that amount would be ok.
Hint: first apply a SMALL amount of tin on the 1st pad. Use a lot of flux. Then put the smd capacitor/resistor on the place. Still a lot of flux there (the component must swim in the flux). With the clean tip do solder the 1st pad. With a SMALL amount of tin on the tip and still LOT of flux there do solder the 2nd pad. Do it fast such the component does not jump off the place. With enough flux and the right tip temperature it takes a fraction of a second.
From the form of the tin blobs it seems you do not use enough solder flux - the components must swim in the flux. From the surface of the blobs I can read - the temperature of your tip is too high.
This is how it should look like (hand soldered) after cleaning the board off the flux (do use an isopropyl alcohol bath and girl/boy_friend's toothbrush):