This is a good guide to claiming PIP and tells you what to do and what to expect:
https://www.turn2us.org.uk/Benefit-g...your-PIP-claim
It sound as if both your Mother and Father should be making their own seperate claims for PIP.
As they seem to be of working age then they should each also consider making seperate claims for 'New Style' ESA (if they have paid enough NI).
Or if they havent made enough NI payments then making a joint claim for Universal Credit with a disability element. (and possibly a carer element).
(They won't be elligible to to make a new claim for Income Related ESA).
Claiming New Style ESA:
https://www.turn2us.org.uk/Benefit-g...port-Allowance
Claiming UC with a health condition:
https://www.entitledto.co.uk/help/Un...ity_Assessment
As both seem eligible for their own seperate PIP (and possibly ESA) claims it does get a bit complicated and I suggest that after reading all that you and your mother/father make an appointment(s) with an advisor local to you who can help with making the different claims.
You can find a local advisor by putting your postcode in here:
https://advicelocal.uk/find-an-adviser
PS. You say that you have "looked around online" - have you tried putting their details into one of the online benefit calculators to check just what they could be entited to?
Try this one:
https://www.entitledto.co.uk/