do I really have to deselect factory 1 by mouse clicking somewhere?
Yes. You can mess with the UI options (or suggest some extra ones), but deselecting first is the default. Off the top of my head you could try any of:
Disable factory grid hotkeys.
Rebind the Select Factory keys to something that does not conflict with construction.
Rebind Select Factory to ctrl+Q, ctrl+W, ctrl+E... since ctrl disables grid hotkeys.
Find or suggest an option to make alt disable grid hotkeys.
These actions can mostly be taken somewhere in Menu/Hotkeys. Disabling grid hotkeys may require Menu/Settings/HUD Panels with Simple Settings unticked (bottom right of the menu).
I don't know how many people use the factory selection hotkeys. It was not bound by default for quite a while. When I bound it personally I set it to Alt+Q because my only use-case is:
Think: I need more constructors.
Mash Alt+Q a few times.
Adding a unit to a factory queue with alt held inserts the order to the front of the queue (without replacing the current construction) and makes it non-repeatable. This makes alt good for making a few one-off units in addition to a factories usual queue.
Later I added Alt+Q to the defaults, and added Alt+WERTY.. because they were there.