Hi Markus,
Yes, OpenAI does have a pricing model. You can learn about their pricing model on their pricing page.
There are certainly good open source alternatives. To start take a look at the trending board of open source models on HuggingFace as a good reference point to begin your exploration. One particular model you can take a look at nomic-embed-text from ollama, but I encourage you to explore all the open source options and find what works best for your needs.
All the best,
Ben