Someone else experinced this because i tried everithing and i just cant make save.I guess the problem is not in the load feature but in the save. I dont have even autosaves and when i click to save nothing happens.
Yes in the begining of the game was free for me too after 50-60 turns though it started to take money so i think this is bug.
For me in the main menu is greyed out and the other option you mention is not possible for me.
Capturing planets requires to build transport ships but first you have to research it.
As title says i cant load game there is save option but no load at least for me its greyed out.