Multiple exposed search filters
There is actually a bug in Search API 7.x-1.8.

The full-text views' filters handler is able to use only one exposed filter (the last one in stack, the previous instances are overwritten).

While it was a LOT of hacking in the Search API module, the simple answer is: you can use only one exposed Search filter in Views with Search API 7.x-1.8 without extensive PHP coding.