Is there a web parser that simulates the experience of playing a text adventure on an old computer (Apple II, C64, PC DOS, etc.), that means “screen” of specific size in characters (usually 80x25 characters, or less for C64 and Apple II), no scrollable command history, monospace font, etc.
Or can Parchment/quixle be configured to operate like this?
With Parchment and Quixe you can use any CSS you want, which should let you do this, yeah.
I’m very bad with CSS though.
Unfortunately I can’t be much help there. But I’m sure others on the forum can; Twine-users tend to have a lot of experience styling their works to look exactly right, in particular.
Here’s a project that builds an game with Inform 6, and wraps it the Parchment interpreter, styled to look like an old VT220 terminal:
Even if you don’t build your game that way, you should be able to extract the CSS and images to wrap your own game.
This is an example of what I did:
http://www.ajmako.com/games/bridge/play-dos.html
http://www.ajmako.com/games/bridge/play-term.html
You could use an emulator. For instance, playing the Pawn on an Amstrad emulator even simulates the delay (and if I remember correctly, the sound) from disc access, and the screen looks exactly the same. Edit: I realise now that this isn’t quite what you were asking about.
Might be a cool project to make a set of css files emulating different terminals/monitors for Parchment 
Another option is to use frotz in Cool Retro Term terminal emulator.
Final thought: there are a lot of great resources for learning CSS, including FreeCodeCamp. It’s a really usable skill and just because you don’t currently know how to do stuff well, doesn’t mean you can’t learn it for the future 
I suppose so, but I’d prefer a full HTML5 parser with simulated screen (a thing that’s beyond my capability as I hate JS with a burning passion). Because no matter how you style Parchment, the text cursor will always be | instead of _.
//edit: There’s this, but with no browser support as far as I know.
caret-shape isn’t part of the css standard at all (although according to MDN, css-color is a legal selector name)—down at the bottom of the page you linked, they show how to get the effect you want using a small amount of css and JavaScript.
It is part of W3C specs: CSS Basic User Interface Module Level 4
Draft, not yet adopted.
Bisquixe may be an option. In particular, examples #18 and #21 in this guide seem to approach what you’re describing.
VT323 and Source Code Pro are two Google fonts I’ve found to be useful for simulating old displays.