This probably belongs in the lore section but it is a fair question.
It is a general question that comes up in every fantasy game - why isn't there more technology? I think it goes back to "necessity is the mother of invention". Tech won't be developed unless there is a need for it and when people have easy access to magic there is less need for technology. What tech there is gets developed by races/groups that have less access to magic than others.
We'd need a 1.0/Garlean lore expert to chime in more but it doesn't look like the Garleans do a lot of magic without the use of assistive technology. As a people they are probably less magically inclined than Eorzeans so they developed magitek to augment their abilities.
I think what the goblins have is different though.
1. If magitek is the cutting edge the goblins are like steampunk. It works but not great with lots of gears and steam power.
2. The goblin devices may not actually be magical. I think they are pure tech. I think the goblins lack the magical ability to actually create magitek.
3. Magitek devices seem to have a life of their own and are sometimes able to act independently. They rely less on physics and more on manipulation of aether and may actually be something like contained/channeled spirits.
To directly address some of your questions:
1. The Ixal have their tech too - airships. They don't seem inclined to want to develop any more. And I think the beast tribes in general depend too heavily on their primals to look elsewhere for power.
2. The citystates do have tech - airships, mammets, and guns. Overall I think they are too used to the magic they have to make adoption of magitek widespread. Magitek also requires manufacturing capabilities that no one currently has.
3. Story-wise I think the Domans would pick it up first since they are more familiar it, they need the extra power, and they have easier access to Cid and the Scions. This might prompt some of the citystates to start investing in it.
4. Gridania is unlikely to want magitek - the sylphs and spirits seem to not like it.
5. Limsa is too dependent on water travel to pick up magitek that is not easily used on water. They would probably love magitek skimmers if someone developed them though.
6. Ul'dah seems a natural place for magitek since there are already a number of mammets in the city and the merchants would be very interested. The political situation makes the adoption of magitek very difficult though. The thaumaturge guild would probably resist adoption of magitek since it would reduce their power. With the struggle between the government and the Syndicate neither side is going to want to openly back magitek since this would cause the thaumaturges to back the other side. I think the most likely scenario is that the Syndicate would secretly start investing in magitek development (with info stolen from the Scions) while publicly denouncing it and planting evidence to implicate the government instead.
7. The new gun class could very well be a magitek class.