How should one handle the identity value and other "obviously" weak secret random values?
In RSA, ECDSA, ElGamal and quite a few other schemes, using a secret (random) value equal to 1 might not provide any form of security, while still being mathematically sound.


One could argue that the exponent '1' doesn't have any security (because it's easy to compute the discrete log of $1G$); on the other hand, you could equally argue that the value $z = 8827773752...7876547109$ equally does not provide any security, because an attacker could easily compute $zG$ and if he sees that, he knows the discrete log.


  Arguably this holds for secret values smaller than 80 bits, as it might otherwise well be attacked using a brute force search attack.


This is true, if the attacker knows apriori that the secret value was smaller than 80 bits.  Actually, if the attacker knows that, he can find the discrete log with $O(2^{40})$ effort, which is doable by private individuals with access to somewhat more than average computational resources.

On the other hand, taking a random $kG$ value, and making that guess will succeed (assuming a 256 bit curve) with probability circa $2^{-176}$.  In addition, this doesn't only apply only to secrets smaller than 80 bits; if the attacker guesses that the top 176 bits are the value $z$ (above), then he can compute $kG - (z2^{80})G$; if his guess is correct, that'll be in the range $0G$ to $2^{80}G$, and so the brute force effort will succeed (and with the same success probability).

Hence, it is hard to say that a point that happens to be in the range $1G … 2^{80}G$ is any weaker than a point that happens to be in the range $(z2^{80}+1)G … (z2^{80}+2^{80})G$ (and all points are in such a range, for some value of $z$).


  do we have some kind of guidelines for the generation of the "secret random values" we have in cryptographic software.


Why, yes, yes we do.  You pointed out the sections in FIPS 186-4 where they make recommendations (mandates, actually, we're talking about FIPS here) on how to generate such random values.


  even though it is crucial for $k$ values to be unbiased.


And these recommendations accomplish precisely that.  They do assume that the approved RBG that is used generates indistinguishable-from-random bit patterns; as far as we know, the approved ones do precisely this.

You appear to be asking for some tests that reject certain values (such as 1); such a test would introduce a bias (if possibly a tiny one); such a bias is precisely what we're trying to avoid...