Karl Bielefeldt's answer is fantastic, but I would also consider the possibility that perhaps your boy is engaging in attention-getting behavior. You mentioned that he is fantastic at home with a special needs and two-year-old sibling. You also said he has previously been getting good grades and judging by your post I'm assuming he's been well behaved up until now. I can relate to your situation both as a parent and as a person who grew up with a special needs sibling. My own 9 year old boy has been having some behavioral issues lately (not as severe as you, but just as out of character.) My brother has severe ADHD and is also brilliant and was, to put it mildly, all-consuming of my parents' time, energy, and focus.
From all of this I have learned that it is easy to take a well-behaved, helpful, smart kid for granted. I felt taken for granted when I was young (actually, I felt invisible and less-loved, but therapy helped me have a more healthy perspective- eventually.) Then, I made the same mistake with my own child, to a lesser degree, but in both cases the result was the same: bad behavior to get the perceived "fair share" of attention. I failed classes on purpose, skipped school, and was an emotional train wreck, having outbursts and tantrums for no reason. A generation later, my boy was acting just like yours, where he's recently developed a bad attitude (talks back, disobeys on purpose, doesn't do his homework, lies about stuff at school) with the difference being he's worse at home. Try talking to your child and see if maybe he feels like nobody is paying attention to him. The fact that he is crying wolf (for instance, he claimed a bully was picking on him) sounds to me like a child who just wants someone to listen and feels as though he has to shout. It may not be the case, but, it's important to get his perspective on this. I may be totally wrong, but it can't hurt to find out. Even though I should've known better, it took my kid getting suspended and a few other deviant incidents for me to hear him "shouting."
Another possibility is that it's not your attention he's seeking. He just experienced a shake up of his social circle. According to this document, children will act aggressively and take risks in order to establish their place in a group. And, they don't necessarily know how to identify or deal with emotions. Your boy may be behaving erratically in response to the new crew at school, which is also likely stressing him out. He may not even know why he's doing what he's doing or feeling what he's feeling. Again, you need to talk to him to find out. Helping him identify his emotions is first step towards learning to deal with them. Then you can work on what triggers them and work on better coping strategies.
Your boy sounds so much like mine...my 9 year old is great great great with his younger brothers, he helps out around the house, is smart, funny, and generally easy going. His brothers are a handful! We were treating him like he was much older than 9, based on his responsible behavior, but he still has the emotional needs of, well, a 9 year old. An 8 (or 9) year old child values respect and acceptance by adults. So, to a certain extent, we were helping him by giving him responsibility, but were hurting him by not rewarding him for his grown up behavior. Praise is very important, so easy to do, so easy to overlook, and, it's free.
Fairness is also high on their priority list. Kids this age are almost obsessive about fairness. They count fruit snacks, turns, and keep track of how many minutes so-and-so got to play on the swings. It might not be conscious counting, but it's there in their subconscious. The lesson he needs to learn is that fair does not mean equal. He's probably smart enough to understand that from a vocabulary angle, but you may need to provide examples. My boy gets upset sometimes that my husband and I spend about an hour getting the little ones to bed, and he gets a 5 min tuck in. We had to point out that he gets a full hour of us to himself every morning before school before the kids get up. Then, it was a non-issue.
Regardless of what motivation your child has for acting out, it needs to stop. I see that you have already gone down the punishment road. Now, I would suggest you try to give your boy appropriate rewards for good behavior. This will most likely be more effective than punishment for bad behavior. Discuss the rewards (whether they are good or bad) for certain behaviors with him. It will help him feel included and respected, and will also make it "fair" since he will have had some input and can anticipate a definite consequence for an action. Let him know that you and the teacher are working together. Good behavior at school means rewards at home, just like bad behavior at school has led to punishment at home. I had to get daily reports from my son's teacher for months. It eventually became weekly reports, and then nothing at all. Each week where he earned good reports every day (good, not necessarily exceptional) he got to stay up an extra hour to watch a movie on Friday night. A single bad day was punished immediately, and, Friday night was off the table. This way, he had a much bigger incentive to behave than misbehave. This is just an example of what worked for us, your house/situation will require your own unique formula.
I would also suggest that you allow him some alone time each day, and schedule one on one time with him too. We were overlooking this with our son, and it turned out to be something he didn't even realize he needed. If school is troubling him lately, he will need some quality down time after school to collect himself and transition to the home environment.
Finally, as Karl mentioned, it may just be a personality incompatibility between your son and the teacher. My son has had two teachers so far that he did NOT do well with. He was a "troublemaker " to both of these teachers, and went from bad to worse pretty quickly, until we all started working together. At the ripe old age of 9, he's pretty much figured out that sometimes people just don't like each other, but you have to get along anyway. If this ends up being all or part of the problem, using the rewards system will still work.
Some folks disagree with the reward system, you can check it out here and admittedly, I find the arguments against it logical, but, like any tool it's all about how you wield it. In some cases, like yours, it can get you "out of the woods" and back on course. It will build confidence at best, and will be a crutch until the school year ends at worst.
I hope this helps.