The prosecutor should have discovery available at your first arraignment date, so if it is coming up soon, you might want to save yourself the headache. As stated above, informal discovery is governed by Penal Code 1054, and is usually a post arraignment issue. I'm assuming that your proactive desire to get your discovery means that you anticipate some holes in your case. If so, I strongly advise you to seek representation, so when you actually receive discovery you know what to do with it....
As stated above, if you were in fact sentenced, the court should have given you a specific surrender date, which you need to find out. That aside, nobody can give you an exact answer to this question. The actual length you serve is determined by many factors, including any restrictions made by the court, and the jail itself. LA County jails are overcrowded and many clients are advised to surrender on Fridays because that is generally when the jails become the most crowded. However, since...
A dismissal pursuant to Penal Code 1385 is in the "furtherance of justice." This usually occurs when evidence is suppressed or brought to light which significantly reduces the likelihood of a conviction if the case were taken to trial. A standard job application should only ask for prior convictions. Here, your case was dismissed, and it did not result in a conviction. So if the question asks you if you've ever been convicted of any felonies, etc., this case should not factor into your answer.
Yes. Assuming he is in fact on an immigration hold, and not being transferred to AZ for some other charge, he needs an immigration attorney to represent him at his removal hearing. Whether he is successful will depend on several factors, including the nature of his conviction. (I added the immigration tag to this question so your question is now viewable by immigration attorneys)
If a video exists, you are entitled to it through discovery, but the LAPD/Sheriff's Department make it very difficult for you to obtain a copy of their dashboard videos. If you were not in fact driving in the manner the police indicated on your report it could be vital to your defense and you should retain an attorney to assist you.
Also, If you are contacted by law enforcement in the future about this incident you should remember that you have no obligation to make any statements, and would be wise to hire a criminal defense attorney.
If you want to resolve this case your only option is to appear. Nothing is set in stone and your best bet is to hire a lawyer to make the best argument possible to keep you out of jail and get you back on your payment plan if you cannot make a payment in full.
You have no legal obligation to pay a civil demand should you get one. Nobody can tell you the chances of a claim being filed against you. Whether or not you pay, Walmart has a right to report the incident to the police, and if the prosecuting agency feels there is enough evidence, they can file charges against you. Should anybody contact you about this incident you have no obligation to give a statement.