Lexically, it is closest to Italian (77% similarity), especially after the 19th-century re-latinization. However, phonetically, it has unique Balkan features.
It's purely etymological. 'â' is used inside words to signal a Latin root, while 'î' is used at the start/end. This was a political decision to emphasize Latinity.
Romanian was isolated from the Western Roman Empire and influenced by the Balkan Sprachbund, which helped preserve the Latin Genitive/Dative forms.
In Romanian, it's more of a 'hybrid' gender: masculine in the singular and feminine in the plural.
They change to make pronunciation easier based on stress and the following vowel.
Yes, many high-frequency verbs follow these patterns.