Only if you're not encrypting many billions of small messages with the same key, which is a possibility. It's just barely large enough for many uses, and "just barely" makes cryptographers nervous.
No. Extended-nonce constructions solve that problem by using the "large" nonce along with the original key to derive a new key. You then have the "small" nonce space plus the key space worth of random bits.
...a variant on that is DNDK-GCM in draft at https://datatracker.ietf.org/doc/draft-gueron-cfrg-dndkgcm/ and a recent presentation: https://youtu.be/GsFO4ZQlYS8 (this is Shay Gueron who worked on AES-GCM-SIV too).