First off, MS Gothic is a monospace font. (Meaning all characters have the same width and move the cursor by the same horizontal distance. Ok, that's a slight oversimplification. Especially when you're dealing with asian characters, there's a possibility of "double-width" characters which are twice the width of "single-width" characters and move the cursor twice as far.) In sites like Lemmy, there are usually ways to tell Lemmy to switch into "monospace" like you did with the first cat art you posted in the body of your post. And that ensures consistency in the output. With non-monospace fonts, it's more of a crapshoot. Arial's "m" might be a different width than Comic Sans', for instance. Typically, sites like Lemmy (or 4chan or Reddit or Facebook or whathaveyou) won't have ways to specify a particular font (different Lemmy clients are also free to use different fonts), so if you composed ASCII art with a non-monospace font and pasted it into a Lemmy post/comment, even if it looks right to you in Lemmy, it may not look right to other viewers of your post. And that's why monospace is popular for these things.

How to make these? I honestly don't know if there are specialized tools for that. Probably just a standard text editor. The examples you posted have some asian characters in them, so a way to input such characters. I'm on a Linux machine and have fcitx set up for Japanese text input. If you're on another OS, I'd expect the way to set up input for asian characters would be different. Alternatively, there are probably unicode character explorers/apps that can be used and don't require quite the learning curve.

As for how to manage these, no idea. I can think roughly about how I might go about writing a program that migth manage these, but I'm not sure if any exist out there currently.