It will be possible to romance multiple desires! Depending on which ones you chose to romance, there will also be a few scenes for that, a few which have already been scripted. For example; if you decide to romance Ruko and Ray at the same time, you're able to encounter an event where they completely clash at each other, since these two absolutely can't stand the other. You're not going to lose affection points for that though.
Building a harem is perfectly possible.
Oh, that's fine! I've been thinking about that too already. It definitely would feel a lot more lively if their expression would change during it (specifically for Ray I've actually already made some different expressions). However, writing the scenes in itself already takes up a lot of time, so I was thinking of finishing that part first and then updating them to be a little more advanced in the graphic part.
Showering is possible already! It takes a bit of random chance though. Upon entering the house, the places for the piano, kitchen, gambling tables, fire place and shower will be randomized. If it hits a number which is assigned to a desire, this desire will appear. if they should happen to be at the shower or bath, you are able to join them. It's not as advanced as you wrote, but I could try to make it a little more interactive in the future.
Also, if you have the easy-mode on, you don't have to re-enter the mansion several times to randomize the characters. There are certain objects you can click on to just reroll the number and at some point, a character will appear. For the shower, you would have to interact with the pissoir for the kitchen with the oven.
I was going to update the Shower scenes with a CG, it wasn't going to stay just bland like it is. Generally, a lot of things about the interactions are still very lifeless right now, which is due to the game being in early access. For now, I decided to pause working on the mansion altogether, since not many seem to have been able to achieve buying it yet, that's why I want to focus more on quests that can bring in money for it.
After I've done a few of the major things in the game (like adding the male character, writing the spicy scenes for every desire in your room in puzzle, creating every dreamscape event, etc) I'll be starting to work on making these kinds of scenes a little more advanced and interactive.