2cents per mile is the approximate worth of a United mile. So the 50,000 miles that you got as a bonus from Chase are worth $1,000. So, if your ticket costs less than $1,000, you can just buy the cash ticket. If you book through expedia, if all the flights are United flights and not All Nippon Airways (ANA), your ticket will be issued by United. If there is a ANA flight, you could have a ticket issued by ANA.

This is for the airlines mile question - The importance of what company/ airline issues the ticket is to determine how many miles you will earn. For example, you have a $800 united ticket base price, based on your United status, you will either earn x5/x7/x8/x9/x11 times the base ticket cost in redeemable miles. You will also earn ~$800 in Premier Qualifying $ attributed and approx 16000 status miles. All details for this are listed on http://mileageplusupdates.com/

As far as your question about which option is better, everyone will tell you what suits you the best, cost wise, experience wise etc.