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Hi, I suggest you do your p1 and p2 separately. It is actually pretty easy to build circuit by truth table if you not need to do it optimally. Just find all rows where result is 1 and construct one And element for each such row with all inputs that are 1 connected directly and all inputs that are 0 ...

did you forget to attach it?

Sorry, somehow I missed this question.
You probably don't have the output of OR gate connected to anything user can see. That is optimized away and not evaluated. If this is not the case, please upload your circuit here I will have a look.

What is the SET output? Why there is a carry on AND, OR operations?

You are right, anything can be unconnected and it is not an error except for memory all the address bits should be connected.

Not really, but you can use descriptions that will be visible on tool tips when you hover mouse over pin or circuit.

Sure, look at menu Edit. There is select free wires and floating symbols for that purpose.

It connects ends of wires. You can use various gestures to merge/split wires. Please see the help pages for more info.
Basic editing: http://www.logiccircuit.org/edit.html
The entire help: http://www.logiccircuit.org/help.html

It the same as just disconnect the input. For And it treated as 1 for Or as 0.

Is it what you are looking for? Please look at the circuit attached
The dash in the probe means high impedance.