I need to create custom form in shopify eshop and the data send via external API. Is there some way how to do that? Or is there some way how to store the custom data and then access it via private app? Thanks a lot!
This really depends on what data you are trying to collect. If you are just trying to collect standard customer info you can create your own form in .liquid and have a webhook forward the info to zapier or create a private app key/pwd and use the Shopify api to pull information.
If you want more arbitrary information you can create or use an app that allows you to create a form and then process that form's responses.
I have a forms app in development that allows you to create a form and use an api to pull data from form submissions or have the form response sent as a JSON email body. (https://knightsofthenet.herokuapp.com/questionnaire/)
Some of the competition will just email the response in their own format and then you have to parse that response (in the past I've done that with mail gun and a node app. This would be a good use case for SES and AWS Lambda as well.