1. Can I use this watch only wallet to receive funds (from exchanges, other people, etc) by creating new addresses
Provided you set up the watch only wallet using the master public key from your cold wallet, then yes, every address your watch only wallet creates will also be created by your cold wallet.
2. Will those new addresses and funds be automatically transferred to the cold wallet?
As ranochigo has explained, funds are not held in wallets, only keys are, but yes, any coins you send to an address on your watch only wallet will effectively be in cold storage, since the relevant private keys are only on your cold storage wallet.
3. If 1 and 2 is yes, can I also create a watch only wallet on my phone to generate new addresses when I need it?
Yes. You can create as many duplicates of your watch only wallet as you like. They will all stay up to date and synchronized provided they have an internet connection.
And in order to spend, I would need to export transaction from watch only wallet, sign it on the cold wallet, then load it online to send?
Yes. You will be able to use any one of your watch only wallets to do this.