Transiting in Abu Dhabi (UK passport) for 20 hours, is this itinerary possible?

A UK passport is valid for a visa on arrival without cost - as stated plainly at the UAE Embassy website. You need to make sure you have a few blank pages (you'll get a stamp); and your passport is valid for more than 6 months.

Ferrari World is around 12 kilometers from the airport; travel time (depending on traffic) can take between 15 and 40 minutes. It is best to hire a cab from the airport.

The park opens at 10 AM, and you can save yourself time (and money) by booking the tickets online.

For the Sheikh Zayed Mosque - visiting hours start at 9, walk through tours are available at 10 AM, 11 AM and 5 PM. There are no fees to visit the mosque; however, there is a dress code.

Visitors should wear long, loose clothing (this means, no tight jeans/sports wear, shorts, skirts (irrespective of the length) etc.) bare shoulders are not allowed - so no sleeveless shirts/tops. No see though clothing; and no clothing with profanity is allowed. In addition, women must also wear a head scarf.

Cellphones should be switched off, there is no smoking, eating or drinking inside; and no food or drink is allowed (this includes water).

From the airport it takes anywhere from 20 - 45 minutes to get to the mosque (depending on traffic).

For your connecting flight; if you already have the boarding passes (which you should), you need to arrive at least 2 hours prior in order to clear customs and immigration on time.

Regarding manners in public - unlike Dubai, Abu Dhabi is a bit more conservative so PDA (public display of affection) should be kept at minimum. You'll be arriving during the "winter" season; so best to wear long sleeved loose fitting clothes while in public. Co-habitation is not allowed for unmarried couples; however in practice you would rarely be caught for this unless there was some other problem with your stay at a hotel.

You can visit Dubai; however traffic is unpredictable. It is 120 KM from Abu Dhabi airport to Dubai Mall - a travel time of one and a half hour each way. If you were planning to visit Dubai, I would suggest heading there first direct from the airport; then budget your time on the way back.

At 1:20 AM though, nothing will be open so the earliest you can expect to do any sort of sightseeing is 8/9 AM. The Abu Dhabi airport hotel is closed for renovations but the napping area is open and available on first come/first serve:

Please be advised that the nap areas will continue to be operational. Travellers(sic) in transit can still take advantage of these facilities, which include cabin and studio rooms with communal bathrooms. Kindly note that these facilities are not available to book in advance, and their availability will be advised upon arrival.

If you book a room at the Premiere Inn Hotel which is directly across the airport - you can also take advantage of their free shuttle services to the Grand Mosque and Yas Island (where Ferrari World is located).