Ingame hotkeys are based on a grid system. When selecting a planet, ship, starbase or fleet the navigation buttons in the bottom center all have hotkeys assigned, starting from Q on the top left. The next button in the same navigation line is W, the next E and so on. You can see the corresponding hotkey for any button that has one by hovering over it with the mouse.
Submenus of planets, ships, starbases or fleets also have hotkeys. These also follow the same pattern, but with the ALT key as modifier. If you select the factories menu of a planet the 'Construct factories' button is the top-left-most interactible element of the menu, so it has the hotkey ALT+Q assigned to it. The button 'Sell supplies' is more to the right so it has ALT+W assigned. This grid scheme is applied to all menus and submenus.
The ingame top navigation also follows this pattern, but with SHIFT as modifier key.

Galaxy right click

When multiple ships are on the same position a menu with all ships on that position appears when hovering over it with the mouse. Since this is a normal mouse-hover the menu disappears automatically when you move the mouse away from it. But if you right click on the ships instead the menu will stay and you can select individual ships by left clicking.

Ship building

Ships are made out of up to 4 components (hull, propulsion, energy weapons, projectile weapons). Each component must be selected in the ship construction submenu of a starbase to build a ship. You can also build each component individually in the corresponding submenus of a starbase to stockpile them. This can get handy if your starbase is under siege by an enemy player. In this case the enemy can steal resources from your planet, so by stockpiling some ship components before hand you build a ship over multiple turns instead of saving resources to build it all at once.