Recent studies have explored DNA-based algorithms for IoT security and image encryption. A similar encryption algorithm was proposed by Al-Husainy et. al. in 2021 Recently, Al-Husainy et al.in 2021, proposed an encryption algorithm based on DNA processes for Internet of Things(IoT) applications. Upon finding low avalanche effect in our experiments, we first report related-key attack and later propose a key recovery attack on full cipher, which generates the complete key with just two plaintext-ciphertext blocks with time complexity of O(1). Upon discovering these serious weaknesses, we improve the security of encryption algorithm against above reported attacks by employing a bio-inspired SBOX and adding some tweaks in the cipher. A lot of research has been done in developing image encryption algorithm based on DNA and chaotic maps. Inspired from the design of SNOW-3G, a well known cipher, primarily used in mobile communications and considering DNA-based functions as building blocks, we propose a new DNA-based stream cipher-Bio-SNOW. We discuss its security in response to various kinds of attacks and find that it passes all NIST randomness tests. We also find that the speed of Bio-SNOW is around twice that of SNOW-3G. Moreover, by means of histogram and correlation analysis, we find that Bio-SNOW offers robust image encryption. These results highlight Bio-SNOW as a promising DNA-based cipher for lightweight and image cryptography applications.