yes
All states use a rectangular flag except Ohio.
There are lots of non-rectangular flags: many of the flags used for maritime signalling are non-rectangular. The only non-rectangular national flag belongs to Nepal.
No, Nepal's flag is the only none rectangular national flag, with the exception of the square flags of Switzerland and the Vatican City. The flag and more details are shown on the related link.
Nepal's flag is shaped like two triangles. See Sources and related links for a picture.
Nepal
nepal
The national flag of Japan is a white rectangular flag with a large red disk (representing the sun) in the center.
Hawaii
Most flags are.
The only current national flag to not be rectangular or square is that of Nepal.
A rectangular flag with stripes of red, yellow and green with a black star in the middle.
There are 49 that do and Ohio uses a pennant.