dem mann seinen wagen

[Anders]

When you in German use the dative + sein/ihr construction instead of genitive, must you then inflect sein/ihr for case?

Heisst es also: Ich sehe dem Mann seinen Wagen.?

And how do you construct with preposition?:

Ich bin in dem Mann seinem Wagen (I am in the man's car)?

[Cedh]

Yes.

Since these constructions are very colloquial to begin with (even in regions where they're common), there are often some contractions though, which in the case of "seinen" make it seem like no inflection takes place:
Ich sehe dem Mann seinen Wagen - [ˌçz̥eːmˌmanza͡e̯nˈvaːɡŋ]
Ich bin in dem Mann seinem Wagen - [ˌçb̥ɪnɪmˌmanza͡e̯mˈvaːɡŋ]
Sometimes you can even hear place assimilation for the final /ən/ in "seinen" (but usually not for the final /əm/ in "seinem"), which would make both of these example sentences come out with [za͡e̯m].

[Anders]

Thanks cedh audmanh for a good answer!

[Jashan]

When you in German use the dative + sein/ihr construction instead of genitive, must you then inflect sein/ihr for case?

Heisst es also: Ich sehe dem Mann seinen Wagen.?

And how do you construct with preposition?:

Ich bin in dem Mann seinem Wagen (I am in the man's car)?

Not an answer to your question, but related:

I know Dutch does this as well (even in 'non-colloquial' speech). I've heard the theory that that's how English got its phrasal possessive:

*The King of England his throne => The King of England's throne
Or *The man I just saw running down the street, his wallet => The man I just saw running down the street's wallet

How about the other Germanic languages? (Being, mostly at this point, the North Germanics?) Do they do this? How common is this type of construction outside of the Germanics?

[Anders]

How about the other Germanic languages? (Being, mostly at this point, the North Germanics?) Do they do this?

Swedish does not use the 'the man his wallet'-construction but Swedish has phrasal possessive. However, I think that phrasal possessive in Swedish is considered wrong according to conservative prescriptive grammar.

Afrikaans uses a possessive construction with 'se'; Ons seun se naam 'our son´s name'.
Is it a too wild guess to asume that it is the dutch his-possessive-construction that is behind this? 'His' in Afrikaans is 'sy', so they don't really use the word 'his'.

[Jashan]

Afrikaans uses a possessive construction with 'se'; Ons seun se naam 'our son´s name'.
Is it a too wild guess to asume that it is the dutch his-possessive-construction that is behind this? 'His' in Afrikaans is 'sy', so they don't really use the word 'his'.

I would assume it's directly related, actually. Dutch pronouns/possessives are funky, being that 1) they have a stressed/unstressed form and 2) dialects do weird things with pronouns in general.

So while in standard Dutch 'his' is 'zijn' [zɛɪn], it's commonly clipped to 'z'n' [zn]; properly 'yours' (pl) is 'jullie', but what it actually comes out as depends on dialect and the phase of the moons of Pluto. (In Waaslands dialect it was 'ulder' or 'gulder', can't remember which, and I have NO IDEA how 'jullie' ended up as 'ulder').

So it could very easily be that Afrikaans 'sy' is the normal stressed form, and 'se' is descended from an unstressed variant.