If you were trying to illuminate an object in the dark, you would say "Shine some light on that." Shine is the most appropriate verb. You could also say "Get some light on that." or "Put some light on that." but both of those would be less natural and less exact than the verb 'shine'. 'Get' and 'put' in that context would mean something like 'Do what you have to in order to illuminate that object.'
"Shine some light on that object" means direct a beam of light onto an object from a lamp or a flashlight.
You would never use 'throw' in that context.
'Throw some light' is a metaphor only used for explaining something. You're not actually throwing light, the way you are actually directing light with the verb 'shine'.
Another metaphor for explaining something or revealing information about something is to 'shed some light'.
Example: "Gentlemen, let me shed some light on this situation. We can't use either of the exits. We're trapped." You can also use 'put some light' in this context.
Another time you would use 'throw' is if you are telling someone else to illuminate something.
"Throw every light you have onto that ship!"
"Dump every light you have on that airstrip!"
These are colloquialisms that depend on context. A native speaker would understand that you were not telling him to physically hurl all available lighting devices onto the deck of the ship in question or onto the airfield.
Here's a video that makes fun of this:
Pour every light onto that field!
As for your second question, yes, you would say "Straighten that bedsheet."