Yes, invoices are automatically generated at the end of each billing cycle and appear in your Billing History, where you can view and download them.

Is the price fixed, or are there additional charges?

Railway billing has two components: a flat monthly subscription fee (e.g. $5 for Hobby, $20 for Pro) and usage-based charges for CPU, memory, network egress, and volume storage that vary based on what your services actually consume. Your subscription fee includes a credit toward usage ($5 on Hobby, $20 on Pro), so you only pay extra if your resource usage exceeds that included amount. Full pricing details are at railway.com/pricing.