If I have 31 inputs on my wallet and send everything to a new address. My new address will have only 1 input and so on I can have small transaction fees because of less transaction size?
Short answer yes. Consolidating inputs is just spending all the inputs used in the tx to one output (which, goes to yourself so you have 1 input to spend onwards). It doesn't even need to be a new address, just one that you control. Note, you keep having to consolidate future inputs you receive, it's just part of fee/wallet management (with a small loss of privacy).
I used to do this about once a month or when I have more than 20. Mempool hasn't been this low for months, so you should go read Loyce's thread above if you want to take advantage of this (possibly temporary) network situation.
