Solutions:

1.
SELECT 
  Sale_ID, 
  SKU_Code, 
  Gross_Amount,
  LAG(Gross_Amount) OVER (PARTITION BY SKU_Code ORDER BY Date) AS Previous_Amount
FROM Sales_Transactions;

2.
WITH DailySales AS (
  SELECT Date, SUM(Gross_Amount) AS Daily_Sales
  FROM Sales_Transactions
  GROUP BY Date
)
SELECT 
  Date,
  Daily_Sales,
  AVG(Daily_Sales) OVER (ORDER BY Date ROWS BETWEEN 2 PRECEDING AND CURRENT ROW) AS Moving_Avg_3day
FROM DailySales;

3.
SELECT 
  Customer_ID,
  Date AS Current_Sale_Date,
  LEAD(Date) OVER (PARTITION BY Customer_ID ORDER BY Date) AS Next_Sale_Date
FROM Sales_Transactions;

4.
SELECT 
  p.Category,
  s.Date,
  SUM(s.Gross_Amount) AS Daily_Sales,
  SUM(SUM(s.Gross_Amount)) OVER (PARTITION BY p.Category ORDER BY s.Date) AS Running_Total
FROM Sales_Transactions s
JOIN Products p ON s.SKU_Code = p.SKU_Code
GROUP BY p.Category, s.Date;

5.
WITH SaleChanges AS (
  SELECT 
    Sale_ID,
    Gross_Amount AS Current_Amount,
    LAG(Gross_Amount) OVER (PARTITION BY SKU_Code ORDER BY Date) AS Previous_Amount
  FROM Sales_Transactions
)
SELECT 
  Sale_ID,
  Current_Amount,
  Previous_Amount,
  ((Current_Amount - Previous_Amount) / Previous_Amount) * 100 AS Pct_Increase
FROM SaleChanges
WHERE ((Current_Amount - Previous_Amount) / Previous_Amount) > 0.5;

6.
SELECT 
  Operation_ID,
  SKU_Code,
  Quantity,
  SUM(CASE 
        WHEN Operation_Type = 'Inbound' THEN Quantity
        WHEN Operation_Type = 'Outbound' THEN -Quantity
        ELSE 0 
      END) OVER (PARTITION BY SKU_Code ORDER BY Operation_ID) AS Running_Inventory
FROM Warehouse_Ops;

7.
WITH MonthlySales AS (
  SELECT 
    EXTRACT(MONTH FROM Date) AS Month,
    SUM(Gross_Amount) AS Monthly_Sales,
    LAG(SUM(Gross_Amount)) OVER (ORDER BY EXTRACT(MONTH FROM Date)) AS Previous_Month_Sales
  FROM Sales_Transactions
  GROUP BY EXTRACT(MONTH FROM Date)
)
SELECT 
  Month,
  Monthly_Sales,
  Previous_Month_Sales,
  (Monthly_Sales - Previous_Month_Sales) AS Sales_Difference
FROM MonthlySales;

8.
WITH WeeklySales AS (
  SELECT 
    SKU_Code,
    EXTRACT(WEEK FROM Date) AS Week,
    SUM(Gross_Amount) AS Weekly_Sales
  FROM Sales_Transactions
  GROUP BY SKU_Code, EXTRACT(WEEK FROM Date)
)
SELECT 
  SKU_Code,
  VARIANCE(Weekly_Sales) AS Weekly_Sales_Variance
FROM WeeklySales
GROUP BY SKU_Code
ORDER BY Weekly_Sales_Variance;

9.
WITH DailyQuantities AS (
  SELECT Date, SUM(Quantity) AS Daily_Quantity
  FROM Sales_Transactions
  GROUP BY Date
)
SELECT 
  Date,
  Daily_Quantity,
  SUM(Daily_Quantity) OVER (ORDER BY Date ROWS BETWEEN 6 PRECEDING AND CURRENT ROW) AS Rolling_Sum_7day
FROM DailyQuantities;

10.
WITH CustomerGaps AS (
  SELECT 
    Customer_ID,
    Date,
    DATEDIFF(Date, LAG(Date) OVER (PARTITION BY Customer_ID ORDER BY Date)) AS Days_Between_Purchases
  FROM Sales_Transactions
)
SELECT 
  Customer_ID,
  MAX(Days_Between_Purchases) AS Max_Days_Between_Purchases
FROM CustomerGaps
GROUP BY Customer_ID;

11.
WITH ProductIntervals AS (
  SELECT 
    SKU_Code,
    Date,
    DATEDIFF(Date, LAG(Date) OVER (PARTITION BY SKU_Code ORDER BY Date)) AS Days_Between_Sales
  FROM Sales_Transactions
)
SELECT 
  SKU_Code,
  AVG(Days_Between_Sales) AS Avg_Days_Between_Sales
FROM ProductIntervals
GROUP BY SKU_Code;

12.
WITH DailyTotals AS (
  SELECT 
    Date,
    SUM(Gross_Amount) AS Daily_Sales,
    LAG(SUM(Gross_Amount)) OVER (ORDER BY Date) AS Previous_Day_Sales
  FROM Sales_Transactions
  GROUP BY Date
)
SELECT 
  Date,
  Daily_Sales,
  ((Daily_Sales - Previous_Day_Sales) / Previous_Day_Sales) * 100 AS Pct_Change_From_Previous_Day
FROM DailyTotals;

13.
WITH MonthlyProductSales AS (
  SELECT 
    SKU_Code,
    EXTRACT(MONTH FROM Date) AS Month,
    SUM(Gross_Amount) AS Monthly_Sales
  FROM Sales_Transactions
  GROUP BY SKU_Code, EXTRACT(MONTH FROM Date)
),
ConsecutiveGrowth AS (
  SELECT 
    SKU_Code,
    Month,
    Monthly_Sales,
    LEAD(Monthly_Sales, 1) OVER (PARTITION BY SKU_Code ORDER BY Month) AS Next_Month_Sales,
    LEAD(Monthly_Sales, 2) OVER (PARTITION BY SKU_Code ORDER BY Month) AS Next_2Month_Sales
  FROM MonthlyProductSales
)
SELECT 
  SKU_Code,
  Monthly_Sales AS Month1_Sales,
  Next_Month_Sales AS Month2_Sales,
  Next_2Month_Sales AS Month3_Sales
FROM ConsecutiveGrowth
WHERE Monthly_Sales < Next_Month_Sales 
  AND Next_Month_Sales < Next_2Month_Sales;

14.
WITH DailySales AS (
  SELECT 
    Date,
    SUM(Gross_Amount) AS Daily_Sales
  FROM Sales_Transactions
  GROUP BY Date
),
EMACalc AS (
  SELECT 
    Date,
    Daily_Sales,
    Daily_Sales AS EMA_03  -- Initial value
  FROM DailySales
  WHERE Date = (SELECT MIN(Date) FROM DailySales)
  
  UNION ALL
  
  SELECT 
    d.Date,
    d.Daily_Sales,
    0.3 * d.Daily_Sales + 0.7 * e.EMA_03 AS EMA_03
  FROM DailySales d
  JOIN EMACalc e ON d.Date = DATE_ADD(e.Date, 1)
)
SELECT * FROM EMACalc;

15.
WITH DailyCategorySales AS (
  SELECT 
    p.Category,
    DAYOFWEEK(s.Date) AS DayOfWeek,
    AVG(s.Gross_Amount) AS Avg_Sales
  FROM Sales_Transactions s
  JOIN Products p ON s.SKU_Code = p.SKU_Code
  GROUP BY p.Category, DAYOFWEEK(s.Date)
),
RankedDays AS (
  SELECT 
    Category,
    DayOfWeek,
    Avg_Sales,
    RANK() OVER (PARTITION BY Category ORDER BY Avg_Sales DESC) AS Day_Rank
  FROM DailyCategorySales
)
SELECT 
  Category,
  CASE DayOfWeek
    WHEN 1 THEN 'Sunday'
    WHEN 2 THEN 'Monday'
    WHEN 3 THEN 'Tuesday'
    WHEN 4 THEN 'Wednesday'
    WHEN 5 THEN 'Thursday'
    WHEN 6 THEN 'Friday'
    WHEN 7 THEN 'Saturday'
  END AS Best_Day,
  Avg_Sales AS Avg_Sales_On_Best_Day
FROM RankedDays
WHERE Day_Rank = 1;