Dan-san, cloa513ch2629-san,
continuative form for i-adejctives: [adjective] - final "i" + "kute"
continuative form for na-adejctives: [adjective] - final "na" + "de"
negative continuative form for i-adejctives: [adjective] - final "i" + "ku naku te"
negative continuative form for na-adejctives: [adjective] - final "na" + "dewa naku te"
I think you've heard "kutte" in colloquial speech. The correct pattern is "kute" without
little pause in middle
Let's see with you examples:
1. Kare wa ookikute furui ie ni sunde imasu.
2. Kanojo wa goujasu de kokkei desu.
3. Se ga takaku nakute yasete imasu.
=> I assumed you wanted to say "thin" person by "usui", contrary of "being fat". That's "yasete iru".
Hope this helps!
Natsuko(奈津子),
Team JapanesePod101.com