I don't think that there are too many "and"s in the sentence, but perhaps one of the "provide"s can be changed to "offer", e.g.:
I help individuals, schools, and organisations offer special needs care, care training, and home audits by {providing / giving [CHOOSE ONE]} training classes, caregiver evaluations, and other care-based educational services.
or
I help individuals, schools, and organisations provide special needs care, care training, and home audits: I {give / conduct [CHOOSE ONE]} training classes, caregiver evaluations, and other care-based educational services.
I like the Oxford comma, but it's not necessary. [EDIT]: It's necessary to change "carer" to "caregiver", as David Schwartz suggests in his comment above, though. I misunderstood what you meant by that word "carer" (thought it was supposed to be "career") and offered bad advice about spelling it correctly. People who provide care are normally called "caregivers" in the biomedical world.
If your friend is going to provide lists, there will almost always be a need for an "and" in the list. As long as the "and" isn't used to conjoin separate sentences (e.g., I ate and apple, and I drank a cup of coffee, and then I watched TV, and I fell asleep during the program, and then I went to bed), there should be no problem.
OTOH, if all the sentences have the same syntactic structure, then the CV will be boring.
If the sentences are in the cover letter, then they should have more varied structures. If they're in the CV proper, then don't have to be complete sentences but can be something like this:
Give training classes, caregiver evaluations, and other care-based educational services.
Help individuals, schools, and organisations offer special needs care, care training, and home audits.
Etc.
Best Answer
Grammatically speaking, every comma in that sentence is appropriately placed.
Stylistically speaking, some people find the use of "so many commas" to be offensive or distracting somehow. Since you are using commas for different purposes, you can make use of some other punctuation options for the different purposes.
The most obvious choice is to replace the "parenthetical commas" with actual parentheses:
Alternatively you could go with "parenthetical em-dashes":