+12 or -12 offset?
35x12.50 is a no go with -12 offset. I have a 315/70/17 tire with 4.5" backspace and -12mm offset and had to trim back an inch of metal. Still rubs at full lock. Love the look but wish I went with a positive offset to make it more functional.
I know for a fact the 35/12.5r18s will not fit with a -12 offset. I'm pretty sure I'm running the largest tire for that offset(295/70r18). The +12 offset shouldn't have issues though, it's a 5.5"BS.
Your tires will for sure stick out still just not as much as the -12. I think they'll stick out about 1" - 1.5"
Your tires will for sure stick out still just not as much as the -12. I think they'll stick out about 1" - 1.5"

I'm not sure how much trimming is involved with the Terra's but with my trails I had to trim a bit.

