"Megawati Sukarnoputri"

She's the daughter of onetime Indonesian President Sukarno.

Meaning that the -putri part means "daughter". IIRC, that's from
recent Indic languages like Hindi, with a male counterpart "putra"
meaning "son". Is that correct?

This would mean that the Brahmaputra River in India has a
name that means something like "Brahma's Son".

Also, does the -i suffix being used for the feminine result from
the original Indo-European -a: sounding too much like what -os
turned into in India (-a)?

Which brings to mind the question of how often the close-family
words have been replaced in the IE languages. I mean: father,
mother, brother, sister, son, daughter. English, like the other
Germanic languages, has the full IE set, but Latin has filius and
filia for "son" and "daughter", Greek has adelphos and adelphe:
for "brother" and "sister", with Modern Greek having poulos for
"son". Russian has otyets for "father", but my patience has run
out.