The star symbols (☆★) have many distinct usages (from near-formal to informal) as a pair of typographical symbols which were available from the first edition of Japanese character set standard.
One of the usages of the white star can be named "pop-ification", which contributes little to the meaning, but adds some overall atmosphere of an outgoing kind of cheerfulness.
Your observation:
“☆” is a stylish version of “・”
captures the essence very well. It is typically seen in proper names of songs, works, groups, and people (pseudonyms). It doesn't need to replace a specific symbol, but can be inserted in the middle of any conceived "breaking point" as if a versatile divider (聖☆おにいさん or even 遊☆戯☆王).
The second example you mentioned is something like a sentence-final emoticon. It gives the (often exaggerated) impression of "sunshine", "life of the party", "kawaii", "airhead", "(feigned) innocent", and so on, attributed to either the person's character or the tone of speech. Cf. キラッ☆
Examples from BCCWJ:
や〜ん☆ 美味しいよぉ〜☆ お肉柔らか〜い☆ オクラがネバネバしてな〜い☆
手づくりの雰囲気たっぷりの、ステキ空間☆
転載の場合は、コピーして貼り付け出来ます☆
熱く語りながらのディナー☆ 楽しかったです☆☆☆
As an aside, while ☆ stands for the "light side" (mainstream) of such emotions, the black variation ★ is often employed for the "dark side" (nerdy, 中二病) counterpart.
