No, that's not the problem at all. The problem is that you think a 135 / 1.8, when mounted in front of a 1" sensor (2.7x), becomes a 364.5 / 1.8 and that when a 135 / 1.8 is used on a FX sensor in [1.5x] crop mode, it becomes a 202.5 / 1.8. This is simply false. Completely and totally false.
But I didn't. I directly answered your question. Here's your question again:
At what aperture did I take my second photo?
And my answer was:
The second photo was cropped to an equivalent focal length of 135 mm x 1.5 = 202.5 mm with the same aperture of 75 mm, yielding an equivalent f-number of 202.5 mm / 75 mm = 2.7.
Too many words? I'll shorten it: you took the second photo with an aperture of 75 mm. That's it. That's the answer to your question. Now, what f-number did you take the photo at? That's probably what you meant. Well, if the focal length is 135 mm, which it is, then the f-number is 135 mm / 75 mm = 1.8, which it is. If the equivalent focal length after the crop is 202.5 mm, which it was, then the equivalent f-number was 202.5 mm / 75 mm = 2.7, which it is.
Yes, it is. Put a lens that can shoot f/1.8 on the camera and take the photo. There's another direct answer to your new question. Adding to that answer, if, for example, you put a 135 / 1.8 on an mFT camera, and take a photo wide open, then the focal length is 135 mm and the f-number is 1.8. The aperture is still 135 mm / 1.8 = 75 mm. So, if you want to convert to the equivalent settings for FF, then you apply the crop factor to both the focal length and f-number: 135 mm x 2 = 270 mm and 1.8 x 2 = 3.6. So, a 135 / 1.8 on an mFT camera is a 135 / 1.8. Full stop. However, if you want to know its equivalent in FF terms, it is equivalent to a 270 / 3.6 on FF.