I wrote a description about my Discord server like the following.

I'm not sure about this one. It sounds weird but it might be okay.
Better might be something like "I'm trying to write a description for my Discord server and I'm going to show you two examples."
Or "I've written a description for my Discord server and these two examples are similar to it."
It depends whether you're in the process of writing or you've already set the description, whether they are similar or exact copies. "like" implies similar but I feel they are probably exact copies.

I textalk about languages (including English and Japanese) in English or Japanese on this server.

"text" as a verb is pretty much solely reserved for sending short messages to people on your phone, I think. I would describe what people do on Discord as talking, writing or chatting.

It's for discussion about grammar, etymology, expressions, vocabulary, etc.

I can't logically justify this, but "It's about" for a Discord server just sounds strange to me :)

I'll be glad if you help my English and Japanese study or exchange language topics with me.

I'm a Japanese and learning English.

Minor, but English doesn't usually like to use "-ese" nationality adjectives as nouns. "I'm a German" is fine, but "I'm a Japanese" or "I'm a Chinese" sounds a bit odd. More natural to use it as an actual adjective - he is Japanese, or he is a Japanese person.

I'd like to talk about languages (including English and Japanese) in English or Japanese on this server.

It's for discussion about grammar, etymology, expressions, vocabulary, etc.

See previous :)

I'll be glad if you help my English and Japanese study or exchange language topics with me.

(And I hope Ito play some board games in English in the future. )

Or "I hope I can/will play"