You use the arrow keys to walk.
Z is to interact with things, but sometimes you will have to click the arrow keys in the direction of the thing you want to interact with and then click z, like with collecting dishes and giving the orders in.
There are some things you can click though, like when you interact with the catalogue on Rody's table, you can click to read through it and buy stuff.
Hope this helps and if you need anything else just reply <3