Official documentation on navigating the system without a mouse is provided at help.gnome.org. Keyboard support is far from optimal and confusing. For one thing, the initial focus in the overview may change depending on where the mouse cursor happens to be. When entering the overview, if the mouse cursor is over a window, that window will be in focus. If the cursor is elsewhere, no window will be in focus. The search box apparently is then focus, so a Down or Tab is then needed to see the highlight appear over the left most top window. This makes for unconsistent and unpredicable behaviour. Depending on where your mouse was on the desktop, keys required to navigate to a specific window will be different.
1. is it possible to use the keyboard to switch to the workspace switching sidebar?
No, but there your regular keys to switch desktops (either Super+Up/Down or CtrlAltUp/Down continue to work.
2.When I switch workspaces using the normal workspace-switching keystroke, where is the default focus? I can't switch between app windows until I press the down arrow!
The focus will be on the search box.
Note 2021-10-19: remaining paragraph is not applicable anymore in Ubuntu 21.10 with Gnome 40: for all practical purposes, the arrow/tab keys are dead if the mouse is not over a window
Pressing Down or Tab then moves the highlight to the windows. Note that, while in the overview, the regular application or windows switching key, Super+Tab and Super+`, will bring focus on the windows and allow you to move between windows.
3. Is any of this configurable? I use Vim a lot and it'd be cool to switch windows with the h, j, k, l keys.
dconf-editor allows to change many keybindings. However, as far as I know, it is not possible (without editing source code) to specifically redefine the keys that move the highlight in the overview (i.e. arrow keys and Tab).