I have two problems: I need to have a deeper speaking voice for a character I need to play on stage, and second, I have a great singing voice live, but when it is recorded, I sound like I have a clogged nose and my falsetto sounds like Miss Piggy. Any ideas?
These are issues you should address with a teacher.
Lowering the voice can cause damage and you will need to work very intelligently to develop the physical support and resonance rather than pushing the larynx low or digging too deeply into the vocal cords.
If you sound like you have a clogged nose you need to check the positions of the tongue and soft palate. Try working with o and u vowels to develop a less nasal tone.
Consider staying in your legitimate voice rather than shifting into falsetto.