So is the option of not putting the parents' data available online and also through the application?
Yes, that's correct. Whether you fill your form online or through the app you'll get asked if you are able to provide information about your parents.
Would that create any disadvantage? to submit the form without the parent information?
Yes, if you do it like that your FAFSA form will be submitted but it won't be fully processed and you won't receive an Expected Family Contribution (EFC). In this case, you should contact the financial aid office at the college or career school you plan to attend.