When practicing some commanding vs bots I ran into the problem of my Relay Towers losing their connection when adding a Power Station further up in the link. This did not seem to affect my power, so is my link still there or are all Power Stations linked with each other without the need of a Relay Tower? In other words do all Power Stations share one common power grid or do they each have there own?
Relays are always linked to the closest powersource (powered relay or powerstation) and if they lose that connection (i.e. powerstation or relay got destroyed) they look for other powersources to connect to. The connection is not "lost", it's just not maintained because it's not neccessary.
They will always only connect to one powersource at a time, which explains your image where the powerstation is closer to the relay than the other relay. If you would sell the powerstation, the relay would connect to the other relay again.
If a relay is connected to a powerstation (including via other relays) it is always powered, which means you don't need a connection to your base to power forward buildings, just a connection to a powerstation.
In short, no, the power stations are not linked, they each act as their own source (so I guess in a way you could consider them linked).
Relay towers should draw power from the nearest source, so if a new power station is built closer to a relay, the relay will switch to drawing from that power source. All relays should still have power, unless an object were placed in the the way of the line of sight of a relay (for Empire relay towers, a direct line of sight between the relays must be present).
From your image, it looks like your upper relays switched from their connection with the lower relay to the new power source. The lower relays will still be transmitting power from wherever their source is, or if that source gets demolished, they will most likely draw power from your new power source in the upper part of the image.