3. Usne ek khat likhiya.
4. Usne ek khat likhiya si /hai.
Likha is not a Punjabi word. In Punjabi the word is likhiya. So constructs 3 and 4 are Ok still, but Usne is also not correct word in Punjabi. Usne and likha are used in Hindi/Urdu. The Punjabi word for he is Osne or better Oh'ne ਉਸਨੇ ਇਕ ਖਤ ਲਿਖਿਆ- ਓਹਨੇ ਇਕ ਖਤ ਲਿਖਿਆ ਸੀ