because it'll also take forever to update the file
No, your totally wrong, just the time for cache clean, for avoid this, modify your ".htaccess" file on your hosting account and configure new cache time.
I NEVER make a textarea tag as a self closing
As I can see, the code source on your computer is different from the web page, it's NORMAL, you have put a old and obsolete html code, google chrome just have correct this for you, not the hosting server. Chrome assuming you close with "</textaera>" but is cleary not necessary so, chrome self close the tag, that's it.
All other support I've been able to get with trying to figure out what's wrong say this is a server side issue
I'm interesting to talk with these Other people ... or just, stop to talk to us.
Overall, your thread is a very basic situation all beginner coder get in his life, it's normal, please .. be honest and assume your wrong, don't put the fault automatically on server-side, it's too much easy.
Now, if you understand this, I would be happy to help you to find and fix your code problems. Can you explain again with much more details your problems with your script and/or error you receive.