Why do crypto tools display key components in such an unusual format?
As for the leading zero, I believe the tools are just displaying what's in the ASN.1 as is; the BER/DER encoding rules will insist on a leading 00 byte in some cases.

Specifically, if you encode a positive integer, the msbit of the value stored must be 0 (if it is a 1, the encoded value is assumed to be negative); if the msbyte of the value you want to store has a 1 msbit, then you must prefix a 00 byte byte to the stored value; this 00 byte does not change the value (obviously), but it does make the msbit 0.  In both case you have, the most significant nonzero byte has an msbit of 1; hence, they have a 00 prefix.

Now, you state that other components within the private key do not have a 00 prefix; I expect that, if you examine them, the first byte of those values will be somewhere in the 01-7f range, and so don't need a 00 prefix.