How To Fix This Bug:
If you are experiencing this bug, it might be because your UTF-8 encoded file is encoded with a BOM. To fix this, I downloaded Notepad++, and from the top bar, clicked Encoding > Encode in UTF-8.

Special thanks to jirauser71590 and violine1101 for their help.

Original Bug Report:
So I was playing on one of my worlds that uses a lot of chain command blocks, when I heard about functions. Naturally, I wanted to try them out. I was able to get one of my chain commands to work, but for some reason, others don't the game seems to arbitrarily decide which functions to recognize. I always used /reload to load any changes I made, I always used UTF-8 encoding, and like I said earlier, I got one of my chain commands to work. However, some of my commands don't work, and I have no clue why. I have included the functions I have tried to use and screenshots of them working (or not) to help aid in this bug fixing. Thanks!

Edit:
After looking at the log file (thanks jirauser71590), the error appeared to be that the mcfunction reader didn't believe that "execute" or "tellraw" were valid commands.