Yes, checked luggage is X-rayed and may be subject to further screening.
As of this writing, there are no charges on domestic flights in the US for the first piece of checked luggage. Please check with your airline for recent changes.
yes
It will depend on where you are flying from. Generally shaving gel is considered as a liquid and it should be in checked-in luggage, not in hand luggage.
Yes. I have carrried one in my carryon and checked luggage for international and national flights.
You should be able to, as an ink catridge is less then 100ml, but it will have to go in a plastic bag.
All liquids taken onboard in hand luggage, including alcohol, have a 100ml (3.4 oz) restriction. No limits on checked, hold luggage. See related link below.
Yes alcohol in checked luggage is permisible.
If its in your checked luggage, not your carry ons.
Yes, as long as you clam it and it is not over a serton amount ( about 2-3 bottles)
Immigaration and customs have to be cleared on arrival at LAX. This always has to be done before proceeding to any domestic flights. Having cleared customs, you then have to check in for your domestic flights of drop you bags. Its only Internationl - International, Domestic-International and Domestic - Domestic where you can have luggage checked all the way through and so dont have to check again. There are no check-in desks on the airside as far as I can recall and you would have to use the check-in desks on the ground side. You could always call United to confirm http://www.los-angeles-lax.com/
While traveling by plane is usually faster it still has a few disadvantages. The main disadvantages are some people are scared of flying, delayed flights, altitude changing causing pressure, and the occasional luggage loss.
Not legally in international flights.