This is a dual-pronged question.

Technological levels vary from region to region. In Eorzea, things are pretty low-tech; they don't need a lot of technology due to the ability to use magic. Since they can do that, they don't need to advance their technological level - a lot of tech is developed during wartime and then repurposed or modified for civilian use (i.e. microwaves). I believe it was also mentioned that Lolorito & co. are actively stymieing efforts to advance Eorzean technology as well - the very small railway in Thanalan being the biggest purely technical advancement not reliant on Garlond Ironworks or anything overtly magical (i.e. ceruleum-powered airships) - in an attempt to funnel more money into their coffers by keeping people reliant on the transport methods already in place (that they own).

Garlemald's native population can't use magic, so they had to develop magitek to compensate. Due to the magi- part of magitek it's capable of doing more than real-world technology, but it's all dependent on ceruleum (magical gasoline), so there are limits to it's capabilities.

Medical knowledge is somewhat lacking, though medical techniques are pretty effective. Aside from magic there are known chirurgeons (surgeons), so there must be some basic medical care not involving magic. There are also alchemists, who despite being capable of producing effects impossible in reality (i.e. resurrecting the dead, if only for a moment) have a practice rooted in science. Once again, Garlean ability eclipses Eorzean in this field (and even reality); they have the ability to edit genomes as of Stormblood, at least.

(Side note: oh absolutely the Ascians play the magic / tech sides against each other. Tiamat says verbatim when you meet her that they taught her how to summon "Bahamut" back from the dead, then gave the Allagans the means to capture his Pet Sematary specter. They're doing the same thing with the Garlean Empire, albeit in reverse - get the tech side riled up and on the warpath, then give the magic side the means to summon in self-defense.)