Is there a way to align desktop icons to (a vertical and horizontal) grid?

Right click on desktop, and check 'keep aligned'. This automatically snaps the icons to grid.

I wrote iconic to let you define a grid size to suit your needs. Additionally it will:

• Allow you to move icons to any of three monitors
• Not suffer the "lost icon syndrome" that occurs when monitors of multiple resolutions are used
• Sort icons alphabetically, alphabetically with "Link to" prefix ignored, sort by modified date ascending or date descending
• Allow different grid size (columns x rows) depending on monitor, EG more on 4K monitor than 2K monitor
• Instant Test button for quick experimentation on column x row changes or reserved space changes for monitor left, top, right or bottom areas
• Test button will last for x seconds defined by you, clear all windows before test and restore them after test
• Bash script for easy modifications

You can get the script on github.

Here's the main screen:

Visit the github page for iconic to see all the other screens, explanations and a copy of the script.