You have asked very important questions. Please do not enter into any purchase or sale agreement until you understand the profit & loss statement thoroughly.
While there should be defined answers for each of these terms, there are not. Make sure you ask the seller exactly what inputs have gone into each, as you may be surprised.
Typically, here are the definitions in practice:
Gross Profit: That is the amount of profit in a product, before any expenses (other than what it costs to produce: Cost of Goods Sold). For example, if you sell a widget for $85, and it costs $50 to produce, the Gross Profit is $35.
Net Profit: Take Gross Profit above and subtract all the other costs of doing business: Rent, advertising, employees (if labor is not part of COGS above), insurance, telephone, and on and on.
Cash Flow: This is subject to interpretation. Make sure you ask the other party how THEY define it. Typically, Cash flow is the net Earnings of the company Before Interest, Taxes, Depreciation, Amortization (EBITDA). Because the Buyer and Seller will have different situations for each of these, we net them out for proper comparison.
Many Sellers define Cash Flow and similar terms like Seller's Discretionary Earnings or Cash Flow as the above EBITDA plus discretionary or non-repetitive items, like fringe benefits (owner's use of company car, insurance, telephone, travel, etc.) If the owner wrote off $10000 for a car, and $10000 for a trip to Hawaii that had little to do with business, a true Cash Flow for comparison purposes would be to add those back in. The idea is to get a number for cash flow that the company's operations produces.
Now Generally Accepted Accounting Practices (GAAP) defines Cash Flow differently. They assume the seller did not write off any fringe benefits. The Cash Flow statement adds or subtracts and "Financing" items, like asset sales, loans, prepayments, etc. Simply the CASH flowing in and out of the black box that is a company.
Hope that helps. Bottom line: Ask the other party how THEY defined the terms, to make sure you both understand correctly.