The hourly-vs-flat-rate debate has run for decades in the trades. Plumbers, electricians, and HVAC techs largely moved to flat-rate in the 1990s. Auto repair did it in the 1980s. Handymen, contractors, and IT services are still split. The answer depends less on the industry than on how predictable your jobs are and how much your customers value certainty over fairness.
Some will. The answer is: 'I quote by the job, not by the hour, so you know the price before I start. That way you don't pay extra if I run into surprises.' Most customers prefer this once they understand it.
Bill the original flat-rate, then quote the change-order separately. Document the original scope on the invoice so it is clear what was included.
Yes, with normal disclosure rules. Some states (California, for example) require written estimates above a threshold dollar amount regardless of pricing model. Check your state's contractor licensing rules.