I will start small as suggested but is that correct in saying every four meters you need a power source?
You'll want to do something like this for a very long wrong. Every four meters is just a general ball park guidance, but should be good for a starter.
As well do I need multiple extensions to connect to the control board or do all the strips get connected together providing there is a power source every four meters?
In general, you could go either way. But that control board you mentioned looks fancy and seems like it maybe it does a good job of supporting and synchronizing multiple branches. That setup may be more convenient based on your sketch as it will allow you to set things up in more manageable groups.