For instance if a company is listed on multiple exchanges, then the Mkt cap would indicate the total worth on that exchange.
No, this is not true. Shares are shares - a company is not "split" into pieces on multiple exchanges.
For instance, if a publicly traded company has a Market cap of about $2M, I would have assumed that if somebody was in the process of acquiring the said company, that somebody would have to shell out a sum not much greater than $2M at the end of the deal.
Depending on the situation, it might actually take quite a bit more than the market cap to acquire the company. If the takeover were hostile (meaning that the buyer couldn't come to an agreement with shareholders on a purchase price), then the act of buying shares would naturally raise the price as people hold out to sell at a higher price.
On the other hand, one could acquire 50% + 1 share of the company and own a controlling interest, thus gaining control of the board and effectively control the company, but would still only own half of the actual company.
So what would be a good way to estimate the total worth of a company as the market currently sees it?
In finance, any financial instrument (including the stock of a company) is worth the present value of its future cash flows. A company is no different, but more complicated to measure. How do you estimate what the future cash flows will be? How much do you discount the future cash flows to get a present value? These are matters of opinion and can fluctuate greatly depending on who is doing the estimating.
Market cap is a measure of what the owners of the company on average think the company is worth (provided the stock is trading at a fair value), but that's just one measure.
One can also look at the book value of a company, which indicates what the assets of the company could be sold for less the debt that would need to be paid off. This, too is imprecise since the value on the balance sheet is not always the value that the assets could be sold for.
There are also other measures, such as enterprise value, and value based on certain multiples of financial measures like EBITDA that can be used for rough estimates.
So there's not one answer for the "value" of a company- it depends on the context.