First off, while this chip looks to be good (and I really like those yellow headers), it can't help you with inputs and outputs at the same time. I don't think you had that question, but I wanted to answer it in case you did.
For level-converting digital inputs without extra hardware, you can rig up a voltage divider for the inputs to reduce the 5 V to 3.3 V. 18 K and 10 K should be a good ratio, with the 10 K resistor between the 5 V signal and the 3.3 V input and the 18 K resistor between the input and ground. I haven't tested these values with a raspberry pi, but it works on paper. Feel free to google around to see what others use, and definitely test your circuit with a multimeter before connecting it to the raspberry pi. That combo I gave you will produce up to 3.2 V, but if you want to play it safe, reduce the 18 K resistor to 15 K, 12 K or even 10 K. The raspberry pi detects logic high for anything above 2.0 V.
If you need bi-directional communication like I2C, it will be hard to level-shift without more hardware.
Now, for analog signals (I think this is your real question), there is a guide that describes a rather clever method for measuring analog signals between 0 V and 3.3 V using only the raspberry pi and a comparator like the LM311, which are pretty common. The idea is to generate an analog voltage with the raspberry pi using PWM and comparing that voltage to the input until a nearly accurate value is found.
Here is the link: http://hertaville.com/2014/07/11/adchack/
Remember that you might have to use a resistor network like the one I described to adjust the levels of the analog signals to safe values. The guide looks very thorough and there are schematics and code provided, but I don't know whether it is designed for multiple inputs. Good luck!
Update: I missed the link to your kit. To answer your question more directly, no. It doesn't look like anything in that kit is equipped to read in analog signals. Those boards all appear to have a lot of digital I/O but nothing analog.
