I would like to know why price is greater than average total cost under monopoly. In textbooks, average cost is drawn under monopoly price. However, if the fixed cost is so large, can monopoly get negative profit?
If a firm could only reach negative profit in the long-run, they would be wise to quit the market. This is also true for monopolies. If you accept that firms are rational, if a monopoly cannot attain non-negative profits it will quit the market.
Your idea about the fixed cost being very large is the intuition behind so called "natural monopolies", where the a competitive (price-taking) market structure would not be able to support even a single firm, but a monopolistic one could.
If you're looking for some hypothetical situation in which the monopolist earns $0$ profits. You can consider the demand function $p = 10 - q$. Also suppose cost function is $c(q) = 25$, i.e., there is only fixed cost and no variable cost. In this situation, monopoly equilibrium price and quantity pair is $(p^m, q^m) = (5,5)$ and profits are $0$.
As Giskard has already mentioned in his answer that it is not possible for the monopolist to earn negative profits in the long run (unless the goal of the monopolist is not to maximise profits), but it is possible that the monopolist earns negative profits in the short run. In the above example, if you consider a fixed cost higher than $25$, then the firm will be earning negative profits.