Which airport are you arriving at?
If Heathrow, if your incoming flight is on time, then you will be out of the airport between 3.30 and 4 pm. It takes an hour to get to Windsor by train or say 30 minutes by taxi (with 6 of you, you would need 2 taxis or a more expensive mini bus). Ideally, you need 2 hours to see Windsor castle and it closes at 5.15, with the last entry at 4pm, so this isn't realistically an option, even assuming your flight arrives on time.
Gatwick, Luton, Stansted or London City airports will take even longer to reach Windsor.
You have 2 options - stay near the airport as you will need to be there at 7am Sunday morning for check-in or stay in central London and get up early! If you head straight into central London, which will take c an hour, that puts you at your hotel at say 5/5.30pm allowing for waiting for trains/underground. Add on 30 minutes for checking in, that doesn't leave a huge amount of time to see the sights and grab something to eat, but you will be able to see some of the sights. Sunset is c 6pm at that time of year, assuming you are not there at the very end of the month after the clocks have changed!
Buckingham is a pretty county town 50 miles from London - I presume that you mean Buckingham Palace?
There are a number of walking tours that operate at night or you could take a Hoho bus, albeit for your short timescale, these are not good value. London Eye closes at 6pm, so you will struggle to fit this in. Buckingham Palace and the Houses of Parliament can easily be covered by walking or taking a bus. Please note that the Queen Elizabeth Tower (where the Big Ben bell is located) is covered in scaffolding for several years for maintenance and the bell isn't striking.