3. If you are hired by a design firm what the process is? do you have papers to sign from the design firm? What's my move as a hired graphics designer?
If what you mean here is an agency, usually may trainings naman yan during the onboarding process. May mga SOP na sila on how to deal with clients.
Ano po young mapapayo niyo sakin and mga things and dapat kong alamin na hindi ko po na ask?
Huwag kang mahihiyang gamitin ang mga connections mo. You can ask people you personally know kung meron silang kakilala na kailangan ng graphic designer.
Pwedeng mas mababa sa market rate yung offer mo since less experience pa pero, gaya ng sinabi ni @cydrix, never do it for free. While free service looks advantageous, baka isipin ng client/s na hindi ka bilib sa sarili mong gawa/kakayahan kaya pinapamigay mo na lang.