How does a monopolistically competitive firm determine profit in the short run and long run?

In the short run, profit is calculated by multiplying profit-maximizing quantity (PMQ: quantity where marginal revenue equals marginal cost) by the difference between the price given by the demand curve at PMQ and the costs given by the average total cost curve at PMQ. In the long run, profit is zero because monopolistically competitive industries lack barriers to entry.

What impact does the purchase of equipment on the account have on the balance sheet?

Assets and Liabilities increase.

Under the IS-LM-FE model, what are the short and long-run effects of an increase in government spending.

In short, run, IS curve shifts right increasing short-run output and interest rate. In the long run, prices will increase shifting the LM curve to the left. This will cause the interest rate to increase in the long run while long-run output remains unaffected.