I was wondering if running the following components is possible on a single Arduino Uno. Any guides on theory and application are also welcome, as I am quite new to this.
Yes it is quite doable. Check the web I have seen projects like this published before. You may get lucky and find exactly what you want. We will help you as much as we can. When you get ready post a schematic, not a frizzy picture with your design and include links to "Technical" information on all the hardware devices. I will take a guess in less then a weakened you will have it sorted out.
i.e. temperature is logged to an SD card every minute. It also uses a character lcd display. To save pins, you can have that display running on the I2C bus.
The main difference is the thermocouple amplifier used, but switching from the max6675 to max31856 will be very easy, as you just need to use a different library. One gotcha to be aware of is that unlike max6675, the max31856 only works with ungrounded thermocouples.