Most of your question is about SegWit, not about soft-fork in general.
I also heard people saying that SegWit is actually a block size increase. Wait what? So you can do a soft fork to increase the block size, and Bitcoin Core clients installed in 2015 and never updated will accept those blocks as valid and add those blocks to their Block Chain?
1. SegWit could increase block size through block size because the witness part is removed and the block size have size 1MB or less.
2. Old client will treat those block as valid block, but they don't perform verification on transaction which use SegWit.
So what is to prevent me from doing my own soft fork? Let's call my soft fork SegCash, and then I buy a bunch of mining equipment and start mining my own blocks. Will those blocks that follow my own soft fork rules be accepted by all the other nodes?
There are many aspect which prevent you from doing it, but mainly it's because
1. Community support.
2. How do you make your change backward compatible.