I have three small additions
First:
we don't use such a construction so much as in English.
I agree very much with this and feel that this comment is probably one of the most important things to be taken away from this discussion. To my ears, at least, even simple sentences like
tumhaaraa ghar mere ghar se baRaa hai (with
ghar repeated) don't sound particularly inelegant/redundant/etc in the same way that the corresponding English sentences do if the word "house" is repeated. In practice, I think this repetition is probably what I would both use and expect to hear
most of the time [^1], even when an idiomatic English translation would not involve a repetition.
Second: While I generally agree with the consensus above that
tumhaaraa ghar mere se baRaa hai is "fine," I inhabit circles where the (prescriptively verboten)
mujh_se →
mere se substitution is
very common in speech, so I strongly sympathize with the concern raised in the OP here:
If I said "tumhaara ghar mere se baRa hai", it'd mean "your house is bigger than me". (i.e. "mere se" would be interpreted as "mujhse")
That being said, I'd like to add that the colloquial oblique → genitive substitution witnessed in
mujh_se →
mere se is
not stable across all person-numbers. In particular, I don't recall encountering the substitution
us_se →
us_ke se, so doing the comparison the other way and saying
meraa ghar us_ke se chhoTaa hai doesn't seem to run into the same potential for ambiguity. (But this sentence too, I slightly prefer with a repeated
ghar.)
Third:
res shuruu huii aur ant meN mere dost uske khilaaf jiit gaye.
This is supposed to be a truncated version of "mere dost
us_ke dostoN ke xilaaf...", so I presume you probably meant to write "mere dost
us_ke ke xilaaf..."? (Or maybe we can even fully subtantivize and go with "mere dost us_koN ke xilaaf..."

) Anyway, circling back to my first point, I entirely agree with
@littlepond jii in #4 and
@Qureshpor jii in #8 that attempting to drop the "possessee" in this sentence feels like a particularly "over-aggressive" application of this syntax.
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Footnote:
[^1]: One sort of systematic exception to this that occurs to me at the moment is certain questions that end on the omitted words (eg: hamaaraa ghar baRaa hai yaa us_kaa? tere ghar chaleN yaa mere? kyaa aap sab X ke ghar se aa'o_ge yaa Y ke?). Here repetition does feel decidedly redundant.