Designing 'real' adventures is difficult be you 13 or 50. What you need to do is to help alleviate his fears about this. Tell him you don't expect brilliance just a good faith effort. Tell him you all understand he is new at this and will struggle. Most importantly give him positive encouragement. If he is good at the rules or roleplaying or just making things fun as a player then tell him so. Confidence is the stumbling block for many new GMs.
Now for some more concrete advice for him on design point - I have some Narrating advice at this site
. Just click on narrating advice and there are articles on designing adventures.
I will say that for your brother's situation he needs to build from what he has done. For example, he has been doing gladiatorial combat, well he just needs to build from that. Add some NPCs, figure out why the PCs have been fighting in the arena, and then use his cave complex. How you ask? Well what if the PCs are hired by the arena master to investigate some caves under the arena. Maybe there is a legend of great treasure in those caves hidden there by a famous gladiator of old. Or maybe gladiators have gone missing and signs point to these caves. What we have here is a tight campaign setting, an arena. But this is all you need for a host of adventures, an entire campaign. Scope and grander are overrated. The best GMs can make an awesome adventure from nothing practically. It is all about the NPCs and the impact on the PCs.
Finally, I will say that your first adventures suck. My first adventure to GM was when I was 12 (22 years ago) and it was with the old D&D basic set and I had all the rules wrong, my friends had no clue either, but it was fun enough. None of us had roleplayed before, there was no Internet, and we didn't have older siblings to help, but it was still fun. We only played for a few months, but it set the seed for me for this to be a lifelong obsession. But the adventure I did then was dreadful, but that is just the way it is. I do not believe that GMing is a gift, it is a skill and it takes practice and effort to master. The sooner you start the sooner it will be that you will be able to GM the adventures you want to run.