A: Hello Meow

Can the execution without the browser showing open ?
>>> Yes, we have a Silent mode run, see doc here:
https://rtila.com/docs/run-automations-in-silent-mode-no-browser-opening/

And also , can it work with api automation ?
>>>
Yes we have a Cloud RUN/API see doc here: https://rtila.com/docs/rtila-cloud-api-documentation-updated/
But not all project are able to run on the Cloud for security/privacy/session reasons.
But we are also working on a paid option for self-hosted Cloud so that you can have your own local RTILA API/Cloud.
Otherwise you can install and run RTILA Studion on a cheap Linux or Windows VPS and run your automations 247 for about $10/month for the VPS rental.

And api that is not web base?
>>> Yes it is web based, REST API and webhooks