Kings Cross is currently mostly:
Rest days of
Tues/Wed
Fri/ Sat
Mon/ Tues
Then Monday/Sat or Fri/Sat
as a four weekly repeating pattern.
Morning turns on weekdays have start times between 04:47 and 08:32.
Afternoon turns on weekdays have start times between 12:33 and 16:13.
There are two PM turns that finish after midnight (at 00:09 and 00:37)
Saturdays have more of a spread in the morning with start times up to 10:17.
Also more of a spread in the afternoon on Saturdays with the latest book on being at 17:47. Three finishes after midnight (similar times to weekdays for two of them and 02:06 for the third).
You are rostered to work approximately every other Sunday, but can say you are 'not available' with 7 days notice and they'll find someone else who wants extra overtime to do it.
You'd be early one week, then late, then early, then late, and so on. But a week of nights comes around about every six weeks. You always go back on afternoons after a week of nights.
The work is mostly Inner Suburban, but there is still a fair amount of Outer Suburban and even some non-stop to Cambridge trips.
Having said all that - there is a major timetable change coming in December, with a higher frequency on the Inner Suburban services between Welwyn/Hertford and Moorgate in the evening, and also with them actually going to Moorgate until about midnight (instead of Kings Cross). They will also go to and from Moorgate and run at a higher frequency at the weekends as well, so all the traincrew diagrams will be rewritten and the roster will change to accommodate the extra drivers needed. I expect there will be less Saturdays off than at the moment.
The current arrangement is that you can have a taxi to/from work if your duty starts before 05:00 or finishes after midnight and there is no train you can use at that time for travelling to/from work.
If it's easier for you, if your duty involves travelling to Hornsey Depot at the start of it, to pick up a train, then you can book on there (there's car parking available) providing you arrange it with the Duty Resouces Manager in advance. There is a telephone to book on, signing on sheet, notice case, and weekly notices etc. at Hornsey Depot, so some drivers book on there instead of at Kings Cross when they have suitable duties.