Electrical – Normally closed semiconductor switch

My first test simply lights up a LED when the switch lets the current flow. As my LED is 2V 20mA, a resistor of (3.3-2)/0.02 = 65 Ohm should be enough, but I only have 100 Ohm, it should be ok right?

That will be fine.

The next step is to capture the switch event in the GPIO 5 listening for 3.3v input. I want a max current of 1 mA to flow through my pin, so I pick a resistor of around 3 k-ohm. Say 5k for safe purposes.

You are getting mixed up at this point.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. A typical micro-controller input with optional internal pull-up resistor.

The input impedance (resistance) of a GPIO pin is very high. If you connect it to the V+ it might draw a couple of micro-amps even with no resistor present. This makes it very sensitive to stray voltages or electro-magnetic fields and, if not addressed, can result in random switching of the input on and off. The way to solve it is to add a pull-up or pull-down resistor of sufficiently low resistance to do the job. 10k is usually a good balance between being sufficiently low and not so low that we're wasting power by increased current through it.

The need for pull-ups is so common that most manufacturers include them internally with a configuration option to enable them.

In your third diagram you have the switch on the "high side" which means that you need a pull-down resistor. If the chip doesn't have an internal pull-down you'll have to add an external one. 10k should be fine.

There are normally-closed SSRs available in DIP-8 packages and smaller. For example, the Toshiba TLP4176G(TP,F) which has a 7mm x 4mm footprint roughly, but there are others.

That particular one has an on-state resistance of 15\$\Omega\$ typically (25\$\Omega\$ max). You may have to add a shunt element to improve off-state isolation (the 'off' MOSFETs will have a tiny bit of leakage, and some capacitance) but that is much less of a problem since you will have power available. There are in fact a few SSRs that have both NO and NC elements in one (somewhat larger) package.