NodeMCU Integer vs. Float Firmware what is different?

You gave the answer to your question yourself. The integer version does not support floating point operations nor does it allow non-integer numbers.

In the integer version 3/2 is 1 rather than 1.5.

I've could simply flash the integer version and give it a try, but I'd also like to discuss it. :)

Stack Overflow is a Q&A site and is thus not well suited for discussions. Use the NodeMCU forums on esp8266.com for that.

NodeMCU developer FAQ says: "integer builds have a smaller Flash footprint and execute faster, but working in integer also has a number of pitfalls"

You've found some of the pitfalls with the 32-bit signed int number size limits.
No idea what others there might be, individual software modules may have their own.

"smaller": usually around 13kB of difference on custom 1.5.4.1final builds totaling 369-478kB

"faster": here is a comparison of integer and floating point operations, with the benchmark source if you'd like to run your own. Overall: int operations are almost 8 times faster. The difference might be smaller when the floats are whole numbers.