Our company has staff members with disabilities.

You can also say disabled staff members. It depends if you want to use person-first language or identity-first language. You can read more about it here: https://askearn.org/page/people-first-language#:~:text=Person%2Dfirst%20language%20emphasizes%20the,is%20equally%20appropriate%20depending%20on

A memberOne of our team members is hearing−impaired.

You can also say that this member has hearing impairments, depending on if they prefer person-first language or identity-first language. If they feel comfortable, you can specify if they're deaf or hard of hearing.

TI then I thought, i"If there were globally common sign languages, we could more enjoy world travel."

There are a lot of sign languages out there. I've heard of ASL and BSL, but don't know much about FSL. Here's an article about it: https://education.nationalgeographic.org/resource/sign-language/

Also, we wouldn't need to suffer from learning difficult grammar and pronunciation of foreign languages.

Although that is true, I've heard that there's a lot of nuance with sign languages in terms of facial expressions and movement of the hands. Personally, I think both would be hard, but that's just my opinion.

Our company has some staff members with disabilities.

The original sentence is okay, but this is much more natural

A There is a member of our team who is hearing−impaired.

Then I thought, if there were globaly common sign language, we could morebetter enjoy world travel.

MORE NATURALLY: Our company has some staff members with disabilities.

AOne member of our team is hearing−impaired.

Then I thought, if there were globaly common sign language, we could more enjoy world travel. more easily.

Then I thought, if there wereas a globally common sign language, we could more enjoy world travel more.

Our company has staff membersemploys people with disabilities.

A member ofn our team is hearing−impaired.

I started learning sign language and recently learned easysome (か a few) basic greetings.

Then I thought, if there were globaly common sign languageas a universal sign language (used everywhere in the world), we could more enjoy world travelling a lot more.

Also, we wouldn't need to suffer from learning difficult grammar and pronunciation of foreign languages.

I started learning sign language and recently learned easysome basic greetings.

When we learn how to communicate simple things in a language, we call it ‘basic’ rather than ‘easy’. For example: ‘basic greetings’, ‘basic phrases’, etc.

Then I thought, that if there were globaly commona universal/global sign language, we cit would more enjoy world travelake travelling the world much more enjoyable.

In spoken English you wouldn’t need to say ‘that’ but it’s more appropriate to have when writing English.
If you wanted to write more casually, similar to how people speak you could drop the ‘that’.

‘Universal’ is the term we usually use here. Alternatively, you could say a global sign language.

Also, we wouldn't needhave to suffer fromtruggle learning difficult grammar and pronunciation of foreign languages.

This way sounds more natural

A member of our team is hearing−impairedhas impaired hearing.

I started learning sign language and recently learned some/a few easy greetings.

Then I thought, that if there were a globally common sign language, we could morebetter enjoy world travel.¶
¶
Or Then I thought, were there some globally common sign language, we could better enjoy world travel.

Usually we use “that” after words like “thought” or “said”

Globally common is grammatically correct but personally I would call it a universal language.