Japanese sentences in the Informal Present Progressive

[Mr.Paper]

Some feedback please.

nihongo ga benkyoushiteiru

sandoicchi o tabeteiru

koukou e aruiteiru

kanojotachi wa shinbun o yondeiru

kare no kuruma o untenshiteiru

inu to o hashitteiru

[astaroth]

nihongo ga benkyoushiteiru

I think: ga → wo : 日本語を勉強してる
ga indicates the subject of the verb and a language can't study itself.

inu to o hashitteiru

I am not sure to understand what you mean by this ... that you are running with your dog?

[Hyperworm]

nihongo o benkyoushiteiru
(ga achieves nothing here besides making "nihongo" the subject, incorrectly)

inu to hashitteiru
(to and o don't go together; just use to on its own.)

The rest are fine, unless I missed something ^^

[becki_kanou]

kare no kuruma o untenshiteiru

What you have above is: "(Someone) is driving his car". But I suspect you wanted to say "He is driving the car", in which case it should be 彼(かれ)　は　車(くるま)　を　運転(うんてん)　している。

は is the topic marker, and の is the possessive marker (among other things).

[katafei]

I was reading it like:
'I'm driving his car'
(all sentences seem to be first person)

Actually, I read it like:
'I'm driving my boyfriends car.'
^^

[becki_kanou]

I was reading it like:
'I'm driving his car'
(all sentences seem to be first person)

Actually, I read it like:
'I'm driving my boyfriends car.'
^^

Without context it could be any of the three and your last suggestion is definitely the most likely from a native speaker, but given the other examples preceding it, it's hard to say.