The backup will skip the chain if it's not finished by the time the chained run is triggered.

As a rule, any plan will skip scheduled launch if it's still running by that time.

Is there a way to program the backups in a chain, so the next backup will start after a backup is finished? What I want to reach is to program backup tasks like:
1. Run: Backup system to network share (2 weeks retention. every 2 weeks Sunday full, every day block)
2. Run: Backup data to network share (2 weeks retention. every 2 weeks Sunday full, every day block)
3. Run: Backup system to cloud (4 weeks retention. every first Sunday of the month full, every day block)
4. Run: Backup data to cloud (4 weeks retention. every first Sunday of the month full, every day block)

- I don't want to use hybrid because I don't want to be depended to be the onsite (hybrid) is working
- I want to use different retention for onsite and offsite

Yes, that should work without any problems. You can chain those plans in whatever order you want.

The backup will skip the chain if it's not finished by the time the chained run is triggered.

As a rule, any plan will skip scheduled launch if it's still running by that time. — Matt

Maybe it's my English :-) But I understand here that it will not run if the backup is still running and the next scheduled needs to be started.

So for me that looks like I need to schedule the plans to run when i'm sure they are finished.

You can simply set schedule just for the first plan in the chain without setting up schedule for subsequent plans, that way you won't have to worry about schedule, all backups will run one by one without overlapping.
Of course, you need to make sure that there is a certain time window between the chains.

Ah thats sounds promosing, so I need to setup chaining for 2,3 an 4?

Yes, only the first backup in chain needs to be scheduled, the rest will be triggered one by one upon finishing.