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There are many things wrong here. The 555 is not the right part here.
The "gate resistors" should be closer to 10 ohms not 10k.
In green I drew the ground nodes. They must be connected together.
U1 and U2 do not connect to ground but live on the Source of Q1 or Q2. U1 must connect to the Source of Q1.
Yes. The top transistors or MOSETs need a gate drive that is referenced to the Emitter (Source) of that transistor. (which is not ground)
In post #8 it is hard to make the two "Vcc=18V" supplies. (one shown)
In post #6 the supply is created via the diode and large capacitor Vb to Vs. (ask if you don't understand or read the data sheet) It only works if the output is switching on/off all the time. If you will leave it full on/off for a long time the circuit will not work well. (long time = 10mS)