No. You get one flat number in writing before any code exists, and that is what you pay. Revisions are included, and nothing gets added after launch.
Half when the build starts, half at launch. Care plans are billed monthly. Your free concept costs nothing, and you only pay if you decide to go ahead.
Your domain and hosting are registered in your name and paid directly to those providers. Where we know those costs in advance, they're listed in your quote. Applicable taxes are shown on your quote and invoice.
A new page or feature is quoted separately, as one flat price, before any work starts. Small edits are covered by the optional care plan.