On the path to version 9 from version 7 I am currently on 8.19. Upgrade assistant shows a lot of deprecation issues that needs to be solved first. Mostly older indexes with compatibility version < 8.0. It is possible to click it one by one to replace index and create alias, but is it possible to do suggested actions in bulk? Or could someone provide an api example how to do that without downtime? Much appreciated! 
(post deleted by author)
What is your use case? Are yoiu using time-based indices that generally go read-only as they get old or are you continously updating and/or deleting from your indices?
I believe the upgrade process, whether you let Kibana run this or automate it yourself via the official APIs, involve reindexing data into new indices and then removing the old index before creating an alias. As reindexing works based on a snapshot of the data in the index when it starts, this process can as far as I know not be done without downtime unless some potential data loss (if index is not read-only) is acceptable.
I dont have much experience with elastic and got a one time task to upgrade existing instances. Indices are constantly used although I think can get away with reindexing during the night. Clicking in upgrade assistant seems easy to do, but time consuming. Is there like an api endpoint to execute this action, as I am afraid that I will mess something up when preparing script to create new indices, waiting for tasks, reindexing, deleting etc.
Welcome to the forum ...
... but. tbh, thats a bit of problem. N.x to N.y is usually pretty straightforward. But N.x to (N+1).y is a major version upgrade, what to do if the process goes wrong, without having "much experience"? And you are on N.x to (N+2).y, which is even harder.
The "system indices" are handled with the Kibana tool, though you need to "press the button".
For your own indices, it reindexes only what was in the index when the reindexing task started. Yes, there is an API to do that re-indexing, so you could script most of it. There's a API way to identify all the indices that are the 7.x version, the kibana UI tells you too obviously. And you need be careful with re-indexing, if you were to be careless you might re-index into a used index-pattern and ... confusion.
How long it all takes depends on your load / hardware / count / size of the indices. And if there is data flowing, you probably need stop it temporarily.
Before doing anything, you should make a full snapshot, which is also what the Upgrade Advisor tells you.
Thank you for your comments. When I reindex a large index, can I run reindexing again to copy only changes since last reindexing? Will that be faster than initial one?