5
SELECT  DISTINCT DATE_TRUNC('month', created_at)::date AS reg_month,
       COUNT(user_id) OVER (ORDER BY DATE_TRUNC('month', created_at)::date) reg_users_cnt
FROM tools_shop.users

6
WITH cte AS
  (SELECT CAST(DATE_TRUNC('month', created_at) AS DATE) AS MONTH,
          SUM(costs) OVER (
                           ORDER BY CAST(DATE_TRUNC('month', created_at) AS DATE)) AS cum_cost
   FROM tools_shop.costs
   WHERE CAST(DATE_TRUNC('month', created_at) AS DATE) BETWEEN '2017-01-01' AND '2018-12-31' )
SELECT DISTINCT MONTH,
                cum_cost
FROM cte;

7
WITH
    pz AS ( SELECT CAST(DATE_TRUNC('month',e.event_time) AS date) AS event_month,
                   COUNT(DISTINCT e.event_id) event_cnt
            FROM tools_shop.events AS e
            JOIN tools_shop.orders AS o ON e.user_id = o.user_id
            WHERE e.event_name = 'view_item'
            GROUP BY event_month )

SELECT *,
       SUM (event_cnt) OVER (
                            ORDER BY event_month) AS cumsum
FROM pz

8
SELECT order_id,
       CAST(DATE_TRUNC('month', created_at) AS DATE) order_month,
       SUM(total_amt) AS order_revenue,
       COUNT(order_id) OVER (my_window),
       SUM(total_amt)  OVER (my_window)
FROM tools_shop.orders

GROUP BY order_month,order_id,total_amt
WINDOW my_window AS ( ORDER BY CAST(DATE_TRUNC('month', created_at) AS DATE) )

9
WITH
    pz AS ( SELECT CAST(DATE_TRUNC('month', created_at) AS DATE) AS acq_month,
                   SUM(costs) AS month_costs
            FROM tools_shop.costs
            GROUP BY acq_month )

SELECT *,
       month_costs - LAG(month_costs,1, month_costs) OVER ( ORDER BY acq_month) AS delta_costs
FROM pz

10
WITH pz AS ( SELECT CAST( DATE_TRUNC( 'year', created_at) AS DATE) AS year_name,
                    SUM(total_amt) AS sum_total
             FROM tools_shop.orders
             GROUP BY year_name )

SELECT *,
       LEAD(sum_total,1,sum_total) OVER (ORDER BY year_name) - sum_total
FROM pz