I agree with others. These are two separate concerns.
First, with the disrespect and the refusal to help out: When your son speaks disrespectfully, don't show him that you've become upset. Ignore him, as though you're an Academy Award winning actor. Don't fret, sigh, make eye contact, or yell back. Then when he asks something nicely, respond immediately. Ignored behavior decreases, rewarded behavior increases (and the rewards aren't money or things, they're your attention, interaction, and respectful eye contact).
Now, regarding the refusal to help. I'm assuming you're talking about chores. Make sure they're clearly established, and reasonable. Make sure your standards are clearly explained. For example, if you expect him to keep his bathroom clean, don't just say "clean your bathroom". Instead, explain that towels are to be hung up, surfaces are to be wiped with a disinfectant cloth (those pop-up towels in the canisters that are disposable), laundry in hamper, etc. If you want him to "clean up after supper", then be clear. That means putting dirty dishes in the sink or dishwasher, wiping the table, or whatever. Often our instructions to our kids are vague and difficult to follow.
And make sure his responsibilities are predictable and consistent. It's chaotic for a kid to be told to do different things on different days depending on mom or dad's whims. Of course, there are emergencies (parent is sick, kid's got to make his own sandwich), but on a normal day, it helps to know what is expected on a routine basis. Have a chart or calendar. That way your son knows that every day he's responsible for feeding/walking the dog, hanging up his towel and putting his laundry in the hamper, emptying the dishwasher, whatever.
If he refuses to do anything that he's tasked with that is reasonable and within his capabilities around the house, then he simply loses the privileges that come with living in the home. No wi-fi. No rides to the mall or to friends. No phone. And make sure that the reasons are clear. Everyone that lives in the home has to do their part. Some pay the rent or mortgage. Some do the grocery shopping. Some cook. Everyone can clean and be responsible for their own space or possessions. And in return, the home functions smoothly and peacefully. Explain that if you didn't pay the electric bill or the water bill or the rent, there wouldn't BE a house to live in. And similarly, if he won't pitch in and do his assigned chores, he doesn't get to have a phone, or internet, or a computer, or pretty much anything else except school.
The worrying is another issue. Trying to convince someone who's anxious or worrying that there's nothing to worry about is like trying to convince someone with diabetes that their blood sugar shouldn't be so high. If he seems really worried, let him speak with a trained counselor.
But there are things you can do. My daughter's counselor helped her think about what is a reasonable fear and what is unreasonable. And then he helped her think about how to handle the situation. Example: unreasonable fear: zombies attacking the house. Reasonable fear: fire in the home. Method: say out loud that zombies are in movies, and stop watching zombie movies. Learn relaxing breathing techniques. About the fire possibility, conduct a safety check with your son as the safety inspector (look online for a checklist, such as frayed wires, smoke detectors working, knowing how to call 911 and the home address, establishing a meeting spot outside, etc). Give your son the power over what he's worrying about, if the fear is possible or reasonable. He's afraid of bullies at school? Enroll him in Tae Kwon Do or some kind of self defense. He's afraid of getting yelled at by a teacher for not doing his work? Help him establish an organized study center, get a homework planner, help him set a time for doing homework, set up an area by the door for reminders, his backpack, permission slips, etc.
Bottom line, be consistent, be clear, make your consequences logical and established in advance, give your son power over what worries him, and get him a couple of visits with a counselor so that both he and you have tools to work with. And establish the code for the house regarding disrespectful language (make sure you follow it too), and don't respond to rudeness.