In startup investments like this one the media basically make a simple factor of the percentage an investor gains and the price he's paying for it. There is no value to that number besides nice newspaper titles.

Real evaluation is the same as for any other company, however in a private company you have less data to go with, the data can't be relied upon as much (since the source is mostly the company itself), and all of these risks get increased by the company being relatively new and not profitable yet. In exchange for the risk investors hope to gain similar growth of company value after they purchased their shares. Therefore most investors mostly look for factors that show huge growth chances, instead of looking at traditional health factors.

In the sense that it is a number that is taken to represent how much money someone would have to spend to buy it, but is only loosely correlated to the amount of money you would have to spend if you actually tried to buy it, yes.

It's different in that publicly traded company market caps are usually based on the value of common stock. The valuation touted in headlines for private companies is usually the implied value of a new, privileged block of stock. The common stock is not valued at the same amount.

But, only IPO all those special classes of stock convert to common stock. So in the success case, yes, valuation and market cap are eventually consistent.