Yes you can. I haven't had any problem getting ammo through the internet in Utah. Nobody has said no.
You may be able to order it online or through a catalog but it will be shipped some way other then the US Postal Service.
Yes and no. Ammunition may not be shipped by US mail (exceptions for some extremely remote areas) but can be shipped by UPS or FedEx.
You can't ship it by USPS. You have to use a third party, like UPS, FedEx, DHL, and it has to have the appropriate ORM-D markings.
No, only in the City of Los Angeles
First Class Mail is delivered in three to five days.