Can individual firms produce at minimum average total cost and make maximum economic profits in the long-run?

Yes, in case of perfect competition an individual firm can produce at minimum average total cost and make maximum economic profits in the long run.

In the long run, all factors of production are variable and can be adjusted. Due to free entry and exit of firms, there will be large number of firms in a perfectly competitive market. As a result, prices of the products will be minimized and economies of scale would also be achieved. So, there will be a level of output at which resources are efficiently allocated and average total cost would be minimized.

Also, if an individual firm maximizes its profits by reaching a level of profits equal to the break-even point, then its average total cost would be minimized irrespective of the type of market in which it is operating.