What is the difference between posting a summons and publication? And what does it mean mail to "last known address"?

Publication is different from posting. See also CCP § 415.50 regarding publication which is also specifically mentioned in CCP § 415.45(a). You...

Can I object all evidences which were not disclosed in discovery process?

You should consider a motion to compel rather than letting everything ride on a motion in limine or trial objection. There can be time limits for...

Chinese vendor sued me, pesonally, and the corporation (where i was the main principal) in LA County. any recourse?

It sounds like there are two defendants: you personally and your corporation. You did not mention a guaranty. So the complaint against you...

Can I put according to proof on the JUD-100 instead of the numbers?

Some context would help for giving a better answer. Usually, though, in a proposed judgment/order/etc. you should put in whatever it is you are...

What do I do if I am trying to have someone served with papers but they are in hiding? Are the orders still in effect?

Maybe hire a private process server to try to serve the papers. They may be able to work it harder, especially if you can pay for "rush"...

Missed the 45 day motion to compel period. What now?

There isn't a 45 day time limit if the other side fails to respond to the discovery. You only have the time limit if you are filing a motion to...

When someone being deposed or examined on the stand says "I don't remember", but nevertheless gives a guess, how valid is it?

It doesn't sound like there's much of a dispute or evidence to make a dispute. So that helps you. Weight of evidence is up to the trier of fact...

I got run over by a self-driving car (I'm fine!). They never agreed to show me the black-box data. Can I subpoena them in court?

This scheme is wrong on several different levels. And it probably won't work because they (manufacturer?) can make a claim of trade secrets to...

No, because there was no demand. And the other side doesn't have to tell you anything either. You may still need to disclose the expert on...

How do you calculate service to enter a default judgment?

For counting days in civil procedure you exclude the first and include the last. So if the party was served on October 1st you count day one as...