Are special terminals required for connecting thermocouple wires to a PCB?

Using a terminal block made with ordinary materials is quite sufficient for a relatively modest accuracy system as you're aiming for.

The cold junction compensation depends on the cold junction sensor (in this case, the chip itself) being at the same temperature as the two junctions where the thermocouple wire transitions to copper. In other words, all three should be isothermal- so you want to minimize gradients caused by dissipation on the PCB and by gradients caused by heat flowing down the wires. You can help this along greatly with ground planes or at least pours and by keeping anything that dissipates a lot of heat well away from the T/C block. Keep air currents away from the terminal block too. Of course you will put the chip as close as practical to the terminal block, physically as well as thermally.

There is no great difference between most sensors as far as this goes as most thermocouples are fairly linear (a couple percent) so 1°C error at the cold junction is around 1°C error in the temperature reading.

If the connection is out hanging in the breeze or is at an elevated (for example) temperature, it's better to use connectors that are made of thermocouple materials, and this is typically done for panel-mount connectors and inline connectors. They are usually color coded. In North America we use the ISA color codes, and type K (Chromel-Alumel) is yellow, type J (Iron-Constantan) is black. You could, for example, have a bulkhead K connector and connect that inside an enclosure to the PCB. You MUST use the proper thermocouple extension wire on the inside as well as outside in this example, and it MUST be connected the correct way (if you swap the polarity the error is actually doubled). Keep in mind that red = negative in North America T/C color codes.

Any change in material will introduce an error on the signal. However if the changes are the same (in terms of both material and temperature) on both terminals then those errors will cancel out. So you can use just about any method you like as long as you keep things symmetrical.

Two things to watch out for - Firstly the temperature that is measured is the difference between the thermocouple junction and the temperature where the two wires become the same material, normally the copper trace on your PCB or the terminal block. This means that if you use screw terminals then your cold junction temperature sensor needs to be at the same temperature as those screw terminals. Any difference will be reflected as an error in your measurement.

Secondly be careful of temperature gradients on your PCB e.g. if one terminal is closer to the power supply or further away from some source of airflow it could be a tiny bit warmer which will impact the end result. If the terminals are on the outside of the box and the cold junction reference is inside getting heated by a CPU then you're going to get a big error.

You must change metals at some point, to connect to the 31855.

I order to do cold junction compensation, the 31855 must know the temperature of this point. Any difference between the temperature of this point, and the point that the 31855 senses, will appear as an error in the temperature reading.

The 31855 measures its die temperature as the 'cold junction'. This means that as long as the 31855 and your 'thermocouple wires to copper' junction are at the same temperature, all will be good. This generally means make the junction as close to the IC as possible, and don't have hot components producing thermal gradients anywhere near the IC.