To align vertically or horizontally one side of your shapes, you can select the 2 vertical points you want to align with the white arrow (direct selection tool), and go in the menu "Object" and then select "Path." Then select "Average." A window will open and let you 3 choices; in your case, you want to align vertically, so choose "vertical."
Then that side will be at 90 degree angle. For your vertical alignment, you'll need to do this for all your shapes.
You can also do this with your arrow shape by selecting the 2 points next to the arrowhead, and align them vertically as well.
You can do this on many shapes at once if you want to equalize them all, as long their paths are on the same axis. For example, if you want to align the top of all your 3 shapes, you could select all their top corners and use the function above but select "horizontal" instead. It will align them in "average" so it's not a 100% precise tool but at least the lines will be straight.
The fastest way to proceed with that kind of project is to trace your shapes properly and then duplicate them... and then expanding their side if you need them to be wider! This way you won't need to adjust every single shape.
One good trick when tracing shapes by hand is to always hold the "shift" key when tracing a path or a line; it will create a perfectly vertical or horizontal line. It works in almost every software! Holding the shift key while moving shapes also help to move them in a straight way and that too can be useful for duplicating shapes or aligning them.