Are all integers kept in 2's complement form in all microprocessors?
If there was the keyword "almost" attached to the question then answering it could have been much more easy. As people have mentioned in the comments that nothing can be said with certainty about "all" the processors but yes majority of them do. 

2s compliment is definitely preferable over the 1s compliment as it provides you a better range for instance if you have 8 bits the you can represent numbers in the range -2^7 to 2^7-1 with it (1 bit being for the signed bit). its interpretation also is easy and quick for the processors. 

However for floating point numbers most processors use a different strategy to save them efficiently. This post would fall short if I needed to explain about them but matter of fact they don't use 2s compliment they rather have the concept of exponential, mantissa and signed bit. And there are 2 commonly used variant of these known as the single precision and double precision floating point representation which are technically same and vary only by the range they can represent. If you want to read further about this you can visit https://steve.hollasch.net/cgindex/coding/ieeefloat.html (not my website, but the website explains the whole thing fabulously).

Let me know if I could help you further in this regard.