1. Is it possible to work and go to Vet School?
Depends on how much work you are expecting to do and your school schedule. I know a few people that worked around 10ish hours or so a week for the first 3 years of vet school. Working during clinics is not possible. You won't be able to work a lot but you might be able to get a few hours here and there for the first few years. And work doesn't have to be working in a veterinary setting. You can do any number of jobs.
2. Does being a CVT hurt?
I mean it can if you get bit or scratched.
As for vet school applications, I don't think it necessarily "hurts". How much it helps, I can't say. It will allow you to obtain a job as a certified tech which will get you the veterinary experience needed to apply to vet school. However, you don't need to be a CVT to obtain this veterinary experience. I was not a CVT, worked as an uncertified tech (allowed in the state I was in) and obtained my experience that way. Others simply shadow vets to gain veterinary experience.
3. What kind of questions will they ask me?
As in for an interview for vet school? These questions vary depending on the school. Not really something you need to worry about at this point, but they aren't going to be asking you any technical questions or medical questions (usually). If you place on your application a specific scenario involving something medical then they might ask more about that situation, but they aren't going to ask you what to do if a dog is in metabolic acidosis or anything like that.
4. Does it hurt that I am older?
Well, getting older can result in joints getting cranky and body parts slowly protesting, but I don't think this is what you are asking about.
Being an older applicant doesn't hurt you. Also, how much "older" are you talking? We get quite a few people on here that go... "I am 25 and older, is that bad?" Mid-late twenties is not "older" for vet school applications. When I see "older" I tend to think mid-thirties or above. And no, it doesn't "hurt" you.
5. DVM saying it works to your benefit....
I will disagree with this person's position. While being a CVT will give you exposure to the field of vet med and experience, the only thing it really does is cost you more $$$ in the long term and makes it take longer to get to vet school. Alternatively, you could just shadow a number of vets to gain experience, finish obtaining your pre-reqs and then apply to vet school. Classes taken at a vet tech school do not apply to vet school. So you are basically doing an extra two years of education by obtaining your CVT that are not necessary and won't contribute to your pre-reqs for vet school. You don't need the CVT to gain veterinary experience needed to apply for vet school.