Why are the dates on financial statements important? How do the primary financial statements (income statement, balance sheet, and cash flow) tie together? What managerial assessments can you make about a company that has a profit and a negative cash flow in the same accounting period?

Why are the dates on financial statements important?
Dates are extremely important for financial statements as the main purpose of financial statements is to reflect the performance of an organization for a certain period and how the assets and liabilities are positioned at the end of a particular period. In the absence of dates, financial statements will not be of any use and its users will not be able to interpret it in correct manner.

How do the primary financial statements (income statement, balance sheet, and cash flow) tie together?

The income statement shows the profit/loss made by company during the financial year. It displays all the revenues earned by the company along with total costs incurred by the company for earning these revenues and thus, the sebsequent result of the operations of the company during a particular financial year. The profit or loss calculated by the income statement is added or subtracted from the statement of retained earnings. Statement of retained earnings, also known as Statement of owners' equity, is one of financial statements, it explains the changes in company's retained earnings over the reporting period.

Retained earnings appear on the balance sheet under "stockholders equity" and most commonly are influenced by income earned by the company and dividends paid out. The retained earnings account on the balance sheet is said to represent an "accumulation" because of the fact that the figure usually grows from one year to the next.
The general formula can be expressed as following:
Ending Retained Earnings = Beginning Retained Earnings + Investments - Dividends Paid + Income.

Therefore, the Statement of retained earnings uses information from the Income statement and provides information to the Balance Sheet.

source: en.wikipedia.org/wiki/Statement_of_retained_earnings

Balance Sheet provides information to stakeholders of the company about the financial health of the company on a particular date. As mentioned above, the retained earnings is shown in the Balance Sheet under Stockholder's equity.

Therefore, we can say that all these statements are interlinked with each other. At the end of the year, the changes in the income statements leads to changes in the retained earnings, which in turn leads to change in stockholder's equity in Balance Sheet.

What managerial assessments can you make about a company that has a profit and a negative cash flow in the same accounting period?

The major managerial assessment will be that even though the company is operating profitably, it is not managing its working capital in an efficient manner or in other words, it is not efficient in terms of cash management. Though it may not be always true as negative cash flow might be due to huge cash outflow for investment, but it can also be due to factors such as poor credit collection policies, etc. Thus, company needs to strengthen its working capital management policies by looking into areas such as receivables collection period, account payables, inventory turnover, etc. Basically, cash management should improve.