Confusion over Equity Value and Enterprise Value

I've been reading the Rosenbaum textbook and am currently on the 1st chapter. It went over the enterprise value and equity value formulas, but I wanted to get a more in depth understanding of how it works.

I looked at this guide: https://samples-breakingintowallstreet-com.s3.ama…

The guide essentially says to look at EV and EqV questions conceptually based on the definitions. They define equity value as the value of everything a company has(all assets) but only to equity investors. They define enterprise value as the value of the business's core operating assets but to all investors. Anything that affects common stock(issuance, repurchase, and dividends) would change equity value, and anything that would affect business core operations would change enterprise value.

I looked at two scenarios I found online which asked how EV and EqV would be affected:
1. Company issues out $100 in dividends
2. Company finds $100 in the street and keeps it in their bank account

Now for #1, dividends is related to common stock, so equity value changes according to the guide. It falls by $100. There's nothing operations-related here, so enterprise value doesn't change. I was confused when trying to check this answer with the formula though. If equity value is market price * # of shares outstanding, then why would issuing dividends change it? I understand that dividends declared and paid out decrease cash and decrease retained earnings. However, isn't equity value based off paid-in capital accounts and not retained earnings(earned capital)? Do we assume that there is a corresponding decrease in the price per share after dividend issuance that causes EqV to fall by the amount of the dividend? If so, then it would check out because cash falls by $100 and EqV falls by $100 leading to no change in EV.

I had a similar confusion with #2 based on the definition of EqV. EV doesn't change because cash isn't a core operating asset. Using the formula, if cash increases by $100, then something else in the formula would have to increase by $100 to balance it out. I guess the only one that would make sense is EV, but that's where I get confused again. I get cash would be debited and retained earnings credited, but why does equity value change based off retained earnings? Per its definition, EqV doesn't factor in retained earnings directly. I suppose it indirectly would be affected because increase in retained earnings would probably increase the price of shares in the market, but how would that be immediately reflected in EqV after the company pocketing the cash? Is there some hidden thing I am missing from EV including retained earnings?

Here are my questions(in case you didn't want to read the post):
1. Why is EV defined as the value of only the core business operations to all investors? If EqV is the value of all assets to equity investors, why doesn't EV also include all value of all assets since it includes every single investor group?
2. Is EqV different from total stockholders' equity on the balance sheet? If so, why do things that affect retained earnings(like dividends) affect EqV by the exact same amount? Do we assume a perfect/efficient market?
3. EV of 0 does not mean you can purchase the company for nothing correct? My understanding is that EqV is the purchase price to acquire the company, and EV is like factoring in the net transaction price based on the operating assets of the company acquired. Although, the guide from M&I says not to think about it as a takeover price. For example, say a person invested $50 cash and started a company, and you decided to purchase it. Assume no debt. The equity value is $50 and that would be the purchase price to acquire the company. However, EV would be 0 because you have $50 after buying the company, so in effect the net transaction price based on the assets of the business is 0. Is that correct?
4. For shares outstanding in EqV calculation, does that include preferred stock shares or no?
5. For EPS calculation, are preferred stock shares included in outstanding shares in the denominator?
6. What is the best way to truly understand EV or EqV? Do you think the M&I guide in this post is the best way to think about it, or just remember the formulas? What has worked for you to master this concept?

Sorry for the long post; I'm a noob to IB and actually want to understand the material instead of just memorizing. Thanks for taking the time to read this post and respond!