First, you should turn off tech trading, at a minimum, turn off tech brokering. It's a horribly broken mechanic and really shouldn't be in the game at all. This will greatly aid you in your quest for parity without spending all your time micromanaging trade deals to keep up with the Joneses.
This probably sounds extremely critical, but it's only because I lack the need for social graces completely and rarely filter things in a futile attempt to be nice, information carries it's own value. I'm a pretty crappy player myself, I can barely beat gifted, but your basics are completely lacking here. Your planets are shit, they have outputs 200 turns behind where they're supposed to be. Your fleets are also bad. You focused on one damage type, yet you're researching them all, your best weapon available is actually a beam weapon, and your neighbors, the terrans, have no shields.
You don't focus them, research structures next to economic structures, every planet is split between them without picking a focus. You have low populations, Ivalice is the only one at 20 population, 20 is terrible. This planet has 36 morale, that's 16 wasted morale.
Starting from Ivalice, if I were to explain what you're doing wrong, it would go quite simply. This planet should be one of two things, pure manufacturing, or a bit of manufacturing and a wealth focus. You can either put just enough manufacturing, centered around that nice +3 manufacturing tile to get your initial expansion out, and pump wealth from the rest, perhaps making it your economic capital, or just go full bore on pumping out ships and make your capital the manufacturing capital. Your starting planet has an easy +10 to raw production between the bonus 5 and the extra population. You put too much importance on the tile modifiers, trying to utilize both the primary tile boost and the adjacency boost, and this costs you massive amounts of productivity. You put zero importance on the adjacency modifiers of the structures themselves.
If you have a fully ringed +3 manufacturing, +1 wealth adjacency tile, you have two and only two options. The first, is that you make it a manufacturing hub, get your +3 first, and complete the ring for a total level bonus of 27. The second, is that you ignore the plus 3 and make it a wealth hub, and get a level bonus of 30. The two sets of research structures are an abysmal use of real estate, the stadium is utterly superfluous with your minimal population and should be replaced with another farm.
Optimize your planets even moderately well, and you could be making ten times the manufacturing, research and wealth you currently are. You have 16 Durantium not being used, but only one Durantium refinery, that's 48 raw production not being utilized, along with the +2 adjacency where applicable. One of these should, resources allowing, be on every planet you've got, starting with your production capitals, and then moving up your planets from low pop to higher. Your typical bonus to the focused production should be several times the base, and your typical Earth quality planet should have 30-60 population depending on tile layout and features, leading you to have raw production two to three times higher than you currently do, and outputs that dwarf your AI competitors.
Further, you have almost no economic starbases, three economic starbases would give you 30% raw production before upgrades and is almost always feasible to get around a planet. You should be pumping them out around all your best planets, leveling them up for maximum effect, and then spreading out to fill in everywhere you can. With how poor your current structure layouts are, you could probably get more out of the starbases than you are now.
Build the right structures on the right planet, and you can have outputs in excess of a thousand. Seeing Noesis II sitting at 10 food with 30 research and a combined output under 100 is enough to make someone cry. At turn 400, this planet should be doing a thousand plus, with the upper left a ring of farms around a food distribution improvement resulting in 40 plus population, and that central land mass entirely dedicated to research as one hell of an epic technological capital utilizing it's ghost world status and two adjacency bonuses.
