Can I use Elasticsearch free of charge?

If you want managed hosting from elastic.co, they charge you according to several variables. You can find the pricing here: https://www.elastic.co/cloud/elasticsearch-service/pricing

If you want to use the open-source version, stand up your own servers and manage your own deployment, the code is at no cost and can be found here: https://github.com/elastic/elasticsearch

It's super-important to remember that spinning up VMs on the cloud is NOT free. In fact, you might spend more money on cloud VMs than using elastic.co's managed services. Elasticsearch is a memory hog and I found that very quickly, and with minor load, I had to dedicate 4GBs of RAM just for the Java heap space. Under heavy load, you'd have to dedicate more. All of that costs money.

As far as integrating with your mainly-javascript stack, it shouldn't be a problem. This library is very useful: https://www.npmjs.com/package/elasticsearch