No, they are not fast diodes.
I would use a BYV27 (click !) (because i have a few of those available).
The generic 1n4148 diodes aren't fast and as raschemmel pointed out will probably not withstand the currents.
I mentioned fast diodes, as a lot of people building stuff like this aren't aware of their existence and purposes.
The L293 consists of 4 half bridges.
The PDF shows multiple options in 1 schematic.
You can use the L293 in any combination shown, you aren't restricted to those examples.
You can create 2 full bridges with them, 4 half bridges or any combination you like.
If you need to control 1 direction, you can do so with 1 half bridge.
If you need to control 2 directions, you need a full bridge.
If you want to control a stepper motor, you need a full bridge per coil pair.
Most hobby setups with steppers will require 2 full bridges, so one entire L293, which will probably be the reason for the existence of this package (except for the hobby part, very few hardware is produced just for hobbyists).
As you might see from this reply, there's a multitude of motor types available, and they aren't all to be powered the same way.
There are motors available that are made to rotate in a specific direction (most of those also have a gear attached).
But sometimes you just don't have a need for a motor to run in 2 directions.
So then you do not need to use a more complicated way of connecting them.
So you need to know what motor you are going to use before you are designing your electronics.
You need to know the motor anyway, because you also need to know the voltage, but more importantly the (stall) current it will take.
You might find out this driver isn't the best choice for your motor type, or maybe it is.