Section 80D

Yes... Deduction/Claim acceptable.

this deduction is only allowed when payment done through other than cash and bearer cheque

80D include two things
1.medical insurance premium
2.preventive health checkup

Premium can paid by any mode other than cash subject to max 25000/30000(for senior citizens)

Preventive health checkup allowed even if paid by cash sub to max 5000/7000(for senior citizen)

Sum of both should not exceed 25000/30000(for senior citizen)
And if you paid for dependent parent then extra 25000/30000 will be add in 80D

what is amount of deduction under 80D if the assessee pays medical insurance premium for his father who is non resident and his age is 67 years?

Sub to max 30000 allow whether father resident or non resident even allow whether father dependent or independent