Yes, this is very much worth mentioning.

Training agility naturally is rather slow and takes a large amount of food to do properly. Even then it's only possible to reach a certain cap determined by your character's aptitude for agility, which in general will be around 16. Some characters may go as high as 19-20, some will be stuck at a mere 14.

The first two levels of UT will be used for dexterity training, something which the banana peels are excellent for. They do very little damage, but are very light and count as whips, meaning you will get a lot of hits in for each opponent for large amounts of experience in dexterity. Pick up and use any equipment you find, even 0 AV armor is better than nothing. Do not replace your peels yet, but pick up the best weapons you can for the situations the peels aren't good enough for. Take extreme care around intact zombies and humanoids with weapons better than balsa spears. If you've taken more than a couple HP worth of damage, retreat back to the stairs, drop your peels next to them to avoid spoilage and return above ground to run around while your health regenerates.

The constant plant spawns by Genetrix can make life on UT3 a bit dangerous. While the normal carnivorous plants are not a threat, it does not take long for greater plants to start spawning. Upon entering the level, ditch your peels if they still haven't rotted away for some unarmed training, but keep real weapons close. Greater plants are rather dangerous in large numbers without anything to block their attacks with. If you haven't yet found body armor and/or a cloak, make exploring the level quickly your priority. If you find Genetrix's room, leave her be for now.

Once you reach NA again, if you haven't got enough bananas left to get you to bloated + about 20 extra, kick some more until you do. Grab all the bananas, and head to sumo's house. Drop one banana 8 squares south from his door, then one 4 squares away, then one on the door. Get inside and while the sumo runs out after the banana trail, vomit 14 times on the spot he usually stands on. You shouldn't lose strength doing this. Once the sumo comes back, eat up to bloated and wait. The sumo's legs will start dissolving. Once he panics or loses both legs, challenge him by going downstairs. The fight will be very easy. Drop the shirt Decos gives you somewhere, equip the belt and head back to UT3.

If you managed to explore the whole level before heading back to NA, there isn't a lot left for you to do here. If you didn't, keep exploring.

Upon reaching Attnam, first things first: take that encrypted scroll to Petrus. There's nothing more annoying than doing everything else, forgetting to give the scroll to him and leaving.

The first level of GC has nothing special about it outside of being the first of the larger levels. Explore around quickly to avoid losing possible carrots or ommel substances to hungry hedgehogs, but stick around for some skill training on new spawns after finishing. Once you feel there's nothing new spawning, head downwards. If you've been doing well, you're also likely to face Rondol as your first named NPC here.