Some obvious points that come to mind. In my view there is nothing special about a Computer Science Phd Viva that would differentiate it from another subject. There are minor differences between countries in the conduct of a viva so some of the answers are may be UK specific and some general to all Phd defence. For example, in some places the viva is in public and anyone can ask questions. In the UK it is usually held in private and often the research supervisor does not attend and you have a different internal examiner and also an independent chair who sometimes comes from another subject. The external examiner would usually be a national or international subject expert, but there is a degree of variability of panel makeup and regulations.
Yes; you can show off, as if your Phd is very good that would perhaps make you one of the countries or subjects experts in the topic of your Phd. It may be something you can be proud about. However, attempting to show off when the external examiner (another subject expert) thinks you are wrong may be a mistake. You have to read the social cues to ascertain which it is!
Certainly there be be some very in depth discussions. They want to know what you know.
Some do's and don'ts:
- Come prepared, Bring notepaper, pens. Take notes when appropriate. Bring a rough copy of the thesis you can write all over if they suggest a change, or use to show them where in the thesis is the answer to their question.
- Sleep beforehand. Be rested and alert so you can clearly understand what you are being asked.
- Remember the independent chair will be on your side. Their role is to ensure fair play. If you want to take a break, ask for one. Ask for refreshments if you need them.
- Try to attend in person. Even if a remote viva is offered, like with Skype or Facetime this is never as satisfactory as talking across a table. If the viva goes badly you will regret saving a few pounds on that airfare.
- Get into a philosophical fight with the external examiner, or imply the external is an ignorant nincompoop for not understanding your research. It will not go down well, as the external is the representatives of the subject experts. They are expected to know what they are talking about. They outrank you on every scale.
- Expect your supervisor to come running to your aid, speak for you, or tell you the answers to hard questions. They are usually not invited anyway. If you got this far with your supervisors hand-holding you will now find yourself alone and on thin ice. This is you test that you make the grade alone.
- Assume that critical questions mean that they don't like your work or think it not worthy. They just might be testing how fully you understand the implications of your work. Handling critical questions well is a sign of a good candidate.
- Don't take it too personally, which is often very hard. Being critical of your writing does not mean that you or your conclusions are in some way lacking. It is their job to examine in detail and they are only doing their job.
Some general point, which I hope are somehow helpful. Best of luck.
(I answer as an experienced examiner and independent chair).