So in long run if fixed cost is lowered, more firms enter the industry and increase the supply, bringing up industrial output. According to the firm diagram, Average Cost lowered so that the firm output is lower. But why is that? Shouldn't the firm produce more when the fixed cost lowers?
The quantity produced does not depend on the fixed costs. Fixed costs only influence the decision of whether or not to produce, not how much to produce. The individual firm's level of production is determined by MR=MC, independent of fixed costs. Firms will produce less when fixed cost decrease, because, as you point out, more firms will produce (entry in the market). On the aggregate market supply shifts out, so that price declines. For each individual pricetaking firm, the exogenously determined price has declined. Put differently, MR has shift down, resulting in an optimum (MR=MC) at a lower level of production.