As a former non-proof reader I don’t feel abashed at telling you to proof read- It really helps to be taken seriously.

18 lbs in three months.

Thats a big gain in muscle mass. Under the very best circumstances a pound a week (lean muscle) is about the upper limit. so 4lbs/month X 3 = 12 lbs.
My guess is that you’re training for some sort of contact sport? wrestling or football?
You need to start eating six times a day. If I were to give you a place to start it would be Lou’s Testosterone-Advantage Plan. I found that book to be the easiest to follow for nutrition and training guidance. If you get the bigger 18 week version – that should put you in a good starting point come September. I don’t know Lou, but I have the aforementioned T-Advantage Plan, The Book of Muscle and The New Rules of Lifting. Since you posted here I’m guessing you already know about these. I still use some of the recipes described in the TAP and will occasionally go back to its workouts if I need to change up my routines. The movements are fundamental, but NROL does a better job of explaining this than TAP. You may have to get creative using your multi-gym to get the movements right. If you have access to a gym, with free weights and spotters – you will get better results than your home equipment – but you use what you have and keep at it.
Keep a workout and food diary, come September show the Coach how far you’ve come and the gains you’ve made. It may help you at least be put on the team for a provisional time. There is a lot more to address than what I’ve covered here, but you can learn that along the way. Good luck

First, I think 18 pounds of muscle in three months is not a realistic goal. If you are a beginner, you can put on some size, but I don’t think that much.

I have a couple recommendations.

1. Eat more and eat more protein. If you are not gaining weight, you need to increase calories.
Your nutrition details are really vague. What kind of cereal? How much? My basic breakfast (I am am trying to lose fat) is 1/2 cup Oatmeal, 3/4 cup blueberries, 10 grams pecans, 1 c milk and 1 egg.
You lunch sucks. Where are your fruits and vegetables? Also, do you eat after dinner. You should be having something in the evening. And if you are trying to gain, I would recommend a protein shake or something before bed.

2. I think your workout is too advanced for your level. I emphasize that this is my opinion, for what it is or is not worth. I think you would be better served by going to a 3/day a week full body workout. Focus on the basics. Squat, Deadlift, Bench, Overhead press, maybe dips, chins, etc. Compound movements. Get the weight up! If you add 100 or 150 pounds to your squat or deadlift, you will get bigger.
If you are 122 pounds, you shouldn’t be doing tricep and bicep exercises. Focus that energy on bench and chins/pull-ups and your arms will grow. Focus it on squat or deadlift and your arms will grow. Also, for now, I would ditch the separate abs workout.

I

Generally gaining weight is as easy as these three steps.

Eat until food looks disgusting to you. You need tons of calories and protein.

Sleep a ton. Ten hours would be amazing for you.

Train. For a simple plan that really works check this site out: http://www.hypertrophy-specific.com/ Really read the site. Don’t get caught up in all the marketing crap. Don’t just print the work outs out or you will totally miss the point of the routine. It is pretty easy to follow. You can skip the negative stuff and and three months get through the program twice. I personally gain over 20lbs in 6 months on this. It uses a total body workout three times a week like telktrot rec’d.