No. Thats the whole point of TOTP/HOTP. That it should be infeasible, given any sequence of valid codes, to generate future codes or recreate the seed.
The reason is that the TOTP/HOTP algoritm, use HMAC-SHA1 as hash, given the "challenge" (either current UNIX time or a counter of usages) and the secret "seed" as key. The resulting hash output is then truncated according to a very specific rule.
This would mean, in your first case, it would be impossible to do, as multiple valid keys will come up with the "correct" 6-digit code but will turn out to be incorrect as future codes from these "valid keys" will be invalid.
To successfully mount a bruteforce attack against a seed, you would atleast need 2 valid auth codes, possible more, and even in that case, its infeasible (eg, practically impossible) to do it.