Question the First: Is it safe to display the counter value on the client side?
The "counter" is not a secret. While the "secret-key" remains secret, knowing the the current or a recent "counter" value is of no use to an adversary. If the "secret-key" is compromised, then you are in trouble. RFC4226 says a lot about keeping the "secret-key" secret, and nothing at all about keeping the "counter" secret. (And with TOTP, clearly it isn't !)
If an adversary does learn the "secret key" and the "counter", they are in. If they have to guess, and the 8-byte "counter" is randomly seeded, then this starts to look like a brute-force attack. Section 7.1 of the RFC, gives requirements for the authentication protocol P, including:
RP2 - P SHOULD NOT be vulnerable to brute force attacks. This implies that a throttling/lockout scheme is RECOMMENDED on the validation server side.
so there is some additional security in keeping the "counter" securely, but neither the client nor the server is required to do so. And even if the client does, the server might not. And that's not part of the formal security analysis.
The "E.4. A Counter-Based Resynchronization Method" (of the RFC) requires the client to send their "counter", and we have:
RP3 - P SHOULD be implemented over a secure channel in order to protect users’ privacy and avoid replay attacks.
...no mention of securely sending the "counter", except as a side effect.
So, the short answer to your first question is "yes", "yes it is safe to display the counter value on the client side" -- where by "safe" we mean "safe while the secret-key remains secret".
Question the Second: Is the "secret" value always 16 digits?
I'm guessing that this refers to the "secret-key", also known as "shared secret" -- so by digits you mean bytes ?
The RFC section 4, "Algorithm Requirements", includes:
R6 - The algorithm MUST use a strong shared secret. The length of the shared secret MUST be at least 128 bits. This document RECOMMENDs a shared secret length of 160 bits.
So a "secret" of less than 16 bytes is not conformant.