I wish there was an option to turn off the history option or the screen so no one can see what you write.
I live with my parents and don't want them to see what I've written be it a private message or a message to all the people in a game.
It can be irritating when Mom or Dad asks me about what I've written.

Hi,
not exactly something on the Playroom, but if you use Windows 8 or newer, the most popular screen readers, Jaws and NVDA both include an option to make the screen black.

In Jaws, it's called screen shade and if I remember right, it is activated either from the tools menu of Jaws or by pressing Jaws plus space followed by print screen.

In NVDA, if you open NVDA's settings panel and go to the vision category, there is a checkbox to make the screen black. You can also assign a shortcut to it from the input gestures dialog. Pressing it once will make the screen black until the next NVDA restart, and pressing it twice quickly will make it permanent until it has been disabled with the same shortcut.

The newest V3 client also offers you the ability to hide certain messages from the history, but note that if you do this and hide chats for example, you also won't have a way to read any previous message.

Unfortunately I don't have a newer version of windows as I can't afford it yet.
My parents want me to use this one until it's died.

Personally changing to weird colours would arouse suspicion or at least it would for me... You have 2 desktops so why not have something else on desktop 2 such as another website or something else. This would not work obviously for a long time as your opponent would want to play but you could quickly switch from one to the other. I have done this with music if I am listening to music not through the PR.

eventually you're gonna have to get a new version because a lot of older stuff is out of date, but that's a discussion for another day and another section of the forum.
as far as screen shade, I thought it worked on Windows 7 so that could possibly be a way to do it. I don't think it would cause suspicion I mean privacy is important in this day and age.

Yeah I know, but for now this one's all I've got.

The first thing you can do is change the font size from 12 to 8 which is the smallest print you can get, least make it harder to read.

press f10
Go to reading and appearance
go down to font
tab until it says font size
up arrow until it says 8
tab until it says ok if you are satisfied with what you have selected and press enter.

Restore defaults if any problems.

Will windows P and second screen only not work?

Use NVDA Screen Curtain.

As mentioned by james, windows p and Projector only should work for versions older than windows 8. Make sure to switch to computer only when you need to turn the screen on.

This may sound annoying or very bad for me to say but no matter what you do you’re parents will want to know. I doubt that hiding the screen will accomplish much since they’ll realise that you are trying to hide something and maybe restrict you from going on playroom or use your PC without the screen curtain. Parents, no matter what they’re intentions are, will always want the control and reassurance. I mean some parents will be open and give freedom but yours looks like they may want to know more than usual or are over protective or have their own reasons for doing so. Its not up to me to find out why you’re parents are like this but more to shine a different light on the problem. Consider just being honest with them; showing them that you’re conversation is really just casual and not serious as in dangerous. Maybe also go to a different room when playing here or come on when they are busy. The idea of putting a small font may help but trying to take control and putting screen curtain when you’re parents don’t exactly trust you will make it worse.

Well, you can defend your claim by using the it-saves-battery line, because that's quite true.
Furthermore, personally living with parents who respect your privacy, I think they ideally should not have a problem since privacy is a right today, and no one, not even your parents, should be allowed to force opening up upon you.