TL;DR: Yes a modern reader can read this.

Only reason I can’t read the whole thing is image quality + bad hand writing

Arab countries speak completely different dialects. But the thing about these dialects is that they’re unofficial, have no grammar rules and change very often.

Dialects lacking grammar rules means they can’t be taught at schools, so schools only teach standard Arabic (“standard” here is redundant because it’s the only Arabic language).

So people don’t actually use the language but everyone in all Arab countries learns the language in detail enabling them to read stuff like this.

I believe society using dialects of Arabic has channeled natural language change into them (which happens all the time to all languages) which let the Arabic language remain unchanged for many, many years.