You touch on a lot of issues, but first let me address the connection between behavior and diet. V8 Splash is not a healthy choice. The first two ingredients are water & high fructose corn syrup, and it only contains 10% juice. (I think it's called "Splash" because it has just a splash of fruit and vegetables in it. LOL.) Basically you are giving your son a big glass of sugar water whenever you give it to him. I participate in WIC, and V8 Splash is mentioned *by name* on their prohibited list. Spaghetti O's are highly processed and also contain high fructose corn syrup. If your son is misbehaving, it's likely because he is jacked up on sugar and sweeteners.
A child your son's age should be drinking no more than 4 ounces (2/3 cup) of juice each day, and it should be 100% juice, not a "juice drink". Juicy Juice makes inexpensive 100% juices. Dilute juice with equal parts water--this lessens the sweetness, ensures your son is getting plenty of water, and makes the juice "stretch".
Many of the foods geared towards kids are NOT healthy at all. They may contain 100% of this vitamin or extra iron or whatever, but a lot of time it's been injected in (it's not naturally occuring) and these foods also contain junk like HFCS and artificial colors. My mom bought my son some Gerber Graduate Sweet Potato Puffs. The first 2 ingredients are flour and sugar. Nice.
Don't go by what the front label says, or what the commercials say. You have to be smarter than the marketers. Turn the bottle or container around and read the list of ingredients on the back--I can not stress this enough. Ingredients are listed in order of quantity, so the first couple of ingredients listed are what the food is mostly made out of. If an ingredient listed is not something you could find on a farm or garden, or you have no idea what it is, think twice before eating it.
Your son will poop better, behave better, and eat better if you back away from processed foods. I am not saying you should NEVER eat boxed mac 'n cheese or potato chips, but they should be a once or twice a month treat, not something he eats weekly.
You can sort of springboard off of what he already likes. Since he likes Spaghetti O's, why not make him homemade spaghetti with a vegetable marinara sauce. The best "fruit snack" of all is simply fruit. If he's used to the texture of processed fruit snacks, he may like dehydrated fruit, such as raisins, prunes, or apple rings. Try to offer 1 fruit and 1 vegetable at each meal. I don't believe in "forcing" kids to eat anything, but if it's offered again and again and that's all there is to eat, they start trying it, and often they like it. With a picky eater, it's easy to fall back on their one or two favorite foods, but this only makes the problem worse.
All in all, I think your son's pattern of eating--sometimes a lot, sometimes none--is completely normal. Offer him 3 meals and 2-3 snacks each day, and he will eat when he is hungry.
Eating healthier can cost a little extra money, but my philosophy is you either spend the money now on decent food, or you spend it later on Miralax or managing Type II Diabetes.
It does sound like he has cabin fever.... I have to respectfully disagree on the weather--it's spring! We're not talking below zero windchill--it is definitely warm enough to be outside. Put a hat and coat on him and let him run around. At this age, even just 15-20 minutes of outside time can do wonders. If the weather is really not to your liking, just get out of the house. Many community centers and schools have open gym time. The children's section of most public libraries have toys and encourage "free play" and noise. He needs exercise in order to poop good, feel good, and sleep good. ;-)
Putting him in time out for 1/3 of the day is only going to make his behavior worse. He is too young to be cooped up in his room like that. At his age, I think diversion, diversion, diversion is key (vs. punishment). Timeouts are appropriate, but they lose their effectiveness if he has 10/day. Also, a good rule of thumb for timeouts is 1 minute per year of age, so 2 minutes for your son. As another mom pointed out, his room may not be the best place for a timeout.... I saw an episode of Nanny 911 where the nanny bought a small rug and that was the "timeout" rug. The kids had to stand on it when they were naughty, and face the wall and be quiet until the timer went off... Just a thought. Good luck.