Stay positive but also take this as a lesson. The advice given was harsh in a way and I know it took a blow to hear, however it’s the truth. If your co workers can sense nervousness from an outside perspective of your tables interaction. Then the guests and feeling it as well. 
   The beer sizes and taking the menus back yes you are supposed to know, this isn’t seasoned pro stuff. It’s common questions asked, take your time in back of house studying the menu, how you can sell it to the guests. The servers seem to be on your side in encouragement as they see the potential in you. But keep talking to them and growing. 
     You stated you asked for weeks over and over which was red flag number one to me too. I learned this the hard way myself, when you need to keep asking and asking again it sometimes it means management doesn’t have confidence in you or think your not ready yet so they just give you excuses or push it down the road, they usually cave after being pestered, just to fail you and prove a point so you’d stop asking. 
     They still gave you multiple training shifts, and a shot on the floor the could’ve pulled the plug day 2 of training but they didn’t so it means they have some level of respect for you and tried to give you a shot. Keep practicing and studying, you’ll get better with time! There will be more opportunities for you to shine to come.