Pronunciation of H after a vowel, as in brahma, brahman

Hello,

Is the letter "h" pronounced when it comes after a vowel, and before either a vowel or a consonant?

For example: maha, brahma, brahman ? 

I know the "h" is not pronounced if it comes after a consonant, i.e. cakkhu, but after vowels it seems to me it should be, otherwise what are they written so on the first place?

If brahma is actually pronounced "brama", then why not just spell it so, since pali should more or less be written as it is spoken? ( which I understand very well because in my native language every sound is a letter, and literally every letter of a word is pronounced, no more no less).