Hi, StarhunterCZ
1) The Cheats checkbox (means you become a cheater in relationships with girls) in the game preferences disables the ability to choose girls, or in other words, enables the so-called "harem mode".
This option is under development, so we are hiding it without specifying what it does. In the final version of the game it will work as we intended. But for now, it may have bugs.
You can read more about cheat mode in this developer log: link.
2) Yes, we have plans to add a replay scene gallery - and we're already working on it, but we don't have enough people, so progress is slow.
3) Don't worry, you didn't miss anything - the gray icon with the briefcase is one of our next features we plan to add to the game, but for now (at the end of 0.4-P2) it's closed - sorry but i can talk about it now.