Do I just program the rows as columns and the columns as rows? And by lines do you mean either the rows/columns of the board?
I'm sorry. By "lines", I meant the wires. Wires can be called lines too, just like "powerlines" are wires ... And on a PCB, they would be visible as lines on a surface as well, but now you are handwiring.
Which end the ring on the diode is indicates the direction of current. The diode prevents current from flowing the other way.
I assume that you plan to use someone else's firmware especially for a handwired M0110. Then you would have to wire it exactly like how the author of that firmware had done it, or you would have to modify the source code.
You would have to not just swap the values for number of rows and number of columns but also shuffle around the order of your keys in the keymap.
For each layer there would be a C array of all keys. The order of the keys in each such array depends on the layout of your matrix: which lines are rows and which are columns.
Each keymaps layer in TMK and QMK is usually written using a C macro that maps from a (somewhat) physical layout of your keys to the actual layout of the matrix -- the key order. You would then have to shuffle around only in that macro's body to change the order, not in the parameters to the macro.