Electronic – Op Amp as a simple switch

It's hard to tell from that picture, but it looks like you have maybe two wires from the arduino going to the breadboard, and two wires going from the breadboard to that thing on the left. Assuming the thing on the left is the remote control, and that, from what you said shorting its two wires together turns it on, then it's very possible to have, as you say, a transistor that's normally open.

The usual thing would be to use a cheap NPN transistor like a 2n2222 or 2n3904. The collector of the NPN would go to the more positive of the two leads from the remote. The emitter would go to the other remote lead. (Use a DVM to be sure which is which, you can't always count on insulation color!) To ensure that the NPN passes no current when no input is connected, you can put a 50K or 100K resistor across the NPN's emitter and base leads. Then, to get input from the arduino, connect the arduino's ground to the NPN's emitter, and connect the arduino control signal you want to use to the NPN's base through a resistor in the range of 1K to 2K ohms.

A circuit like that should not activate the remote when you disconnect the arduino.

The main issue I see in your schematic is that it looks like your op-amp power pins are not connected to anything. You label them with the VCC, and -12V nets, but you never connect these nets to any power supply that I can see.

For most situations where you use a linear regulator, you want to arrange for the amplifier/feedback circuit (the op-amp in your case) to be powered from the input voltage.

The second issue I see is that the way R4 and R5 are set, you are trying to get an output voltage of

\$ (6.2\ \mathrm{V})\times\dfrac{9000 + 240}{240}\$

which is 238 V, but your input voltage is only 12 V. In a linear regulator, the output voltage must always be less than the input voltage. In your scheme you're even more restricted, because the Darlington scheme of QZ and Q1 your maximum output voltage will be about 1.4 V below the input voltage.

Edit

I'll put my comments on the later versions here so the comments can eventually be cleaned up:

Second version

This is better, but I don't think you can get 10 V out. The AD841 datasheet isn't super clear on this, but I suspect its maximum output is about VS+ - 3 V (see Fig 2 in datasheet). Then subtract off 2 Vbe drops for Q2 and Q1, and you're not going to get more than 7.6 V out of this circuit. An op-amp that has "rail-to-rail" output would work better.

Third version

In this version your feedback resistors are set for a target voltage of 43.4 kV.

Also, be aware if you want to build this in reality, the max power supply of AD8542 is 5.5 V. Applying 12 V to V+ is likely to damage the device. This behavior will probably be ignored by the simulation models

Fourth version

Try reducing R1 to 1.2 kOhms. From the NXP datasheet for your zener, the zener voltage is specified for 5 mA current. Also make sure the simulator is seeing all the connections right around R1. With 12 V on one side, and 0 V on the other, there should be 1 mA through R1, not 24 pA. Are your probes somehow changing the operation of the circuit? Why is there a connection dot at the "bottom" end of R1?