I cannot assign a task to someone else

What you see: Create task offers only Create for myself, or assigning fails.

Why: assigning needs the Assign permission as well as Create and View. A new Member profile has neither Assign nor View by default.

What to do: ask a Super Admin to switch on Assign for your role in Directory → Profiles.

Assigning to a partner workspace: the partner must be connected and accepted. See Connect two workspaces first.