1) Nightmare Torpedoes research takes less research time than Photon Torpedoes. For me, Photon Torpedoes took 3 turns and Nightmare Torpedoes took 1 turn. I researched them right in a row, and Photon Torpedo progress filled about 1/3 with each turn, so there should have been very little carryover research to Nightmare Torpedoes.
2) Various defense modules on a starbase list a certain bonus but give far less actual improvement. For example, shields which list +30 or +45 to shield strength actually give +10 each when applied. Phasors listed +30 to beam attack and Doom Ray listed +45 to beam attack but none of my starbases have more than 75 beam attack with both applied, even though they had 40+ beam attack prior to applying either. End-game starbases with only 60 shield strength is severely under powered vs end-game ships with well over 100+ beam attack. Just one hit from a ship will nullify the shields and do hull damage, meaning shields are basically useless on starbases in the end game. The same can be said for the other defense stats, and the weapon attacks. My ships have 200+ shield strength or other defense stats and if the starbase is only putting out 75 damage per round and I can deliver 150 damage in the first round to the starbase's hull, the base is dead in two rounds and it won't have damaged me at all. Assuming the listed bonus is what each module should provide, the numbers end up being far more reasonable for end-game stats on the bases.
3) Telling ships to auto-explore seems to skip sections of the unexplored fog. I didn't take a screenshot, but basically I discovered areas where my ships where exploring where there was a strip of unexplored fog uncovered which was completely surrounded by unexplored fog and that was right next to other such strips. The ship doing the exploration in that area was not in any of those uncovered strips, but was busy making a new one (which also had fog all the way around it). It was not a survey ship, so you can rule out strange wormhole warping. Inside each uncovered strip, you could see the normal fog of war applying.
4) Loading games seems to take more memory than starting from scratch and playing without shutting the game down. I had a game I started yesterday and played for a significant amount of time. It was using 1,440 MB of RAM when I saved and closed the game. Today, when I loaded it again, it immediately used up 2,719 MB of RAM and eventually got up to over 3 GB of usage. Now it only seems to be using 2,115 MB of RAM, but several races have been killed off since the initial load, so that may have freed some up.
5) This is possibly not your problem, but when I hit next turn, Windows Defender chews up almost 30% of the CPU on my box while the turn is processing. Upon completion of the turn processing, it drops down to just a few percent. Disabling real time protection and telling it not to monitor the Galciv 3 folders and processes seems to eliminate the usage, but perhaps there is something you can do on your end to not trigger it so heavily? Other games don't seem to have this problem for me.