When interviewing arrivals seeking entry, what questions do UK Immigration offices ask?
Also, what will be asked on the landing card?
There is no prescribed set of questions; the IO will be trying to determine if you qualify as a visitor under Appendix V of the rules. So a full interview will cover purpose, length, maintenance, accommodation, returnability, and overstay risk.
Assuming you present a valid passport, your landing interview will go something along the lines of...
Any of these questions can trigger a more intensive line of questioning; or alternatively any of these can satisfy the IO that your intentions are genuine and end the interview there. You didn't mention your job or life-style, but there are slight variations of the interview for students, families, unemployed, people pursuing romantic liaisons, attending job interviews, business meetings, seeking medical treatment, and so on.
The outcome of the interview depends largely upon personal impact and articulation skills along with your document preparation.
If you are successful, the IO will affix an 'entry certificate' to a blank area in your passport. It bestows 'leave to enter' and comes in the form of a rectangular rubber stamp. It summarizes the conditions of your leave and its expiry date. In the argot of UK immigration, this means you have been "landed".
For a detailed analysis of what goes through the IO's mind, you can read "Exploring the decision making of Immigration Officers"
See also removal tag questions
Adding 14 June 2015
When your passport is handed back to you, you should examine your entry certificate and double check your expiry date. If you have questions about your entry certificate (i.e., the black, rectangular stamp) or any codes written on it, it's fine to ask the IO what they mean.
People arriving with entry clearances (i.e., visa nationals) can expect some of the introductory questions, but the landing interview will be not as intrusive because the UK has already checked you out and given you permission to enter.