Can one repent from abandoning prayer altogether without repenting from abandoning it sometimes, such as repenting from abandoning all prayers while continuing to abandon the dawn prayer? And does the ruling of the impermissibility of repenting from similar sins while persisting in committing some of them apply to this matter?

Scholars differed concerning the validity of repentance from one sin while persisting in another. Ibn al-Qayyim preferred the view that repentance from a sin is not valid if one persists in another sin of the same type. Furthermore, abandoning prayer is one sin, and persisting in abandoning some of them is considered persistence in a major sin. Please refer to Fatwa (definition) no. 173749. And for those who do not consider one an unbeliever except by absolute abandonment [of prayer], it necessarily follows that whoever regularly performs some prayers but not others is judged to be a Muslim.