Is it valid for someone praying alone to have two intentions, such as the intention of giving charity and the intention of performing the post-prayer regular sunnah (ratibah), or does each act require an independent intention?

It is permissible to combine two intentions in prayer because the majority of scholars hold that a repeated prayer is a supererogatory (nafl) prayer, and the obligatory (fard) prayer is the first one. An act of worship intended for its own sake cannot be subsumed under another, unlike an act not intended for its own sake. Thus, praying with the intention of giving charity to a solitary worshipper is a supererogatory act that can be subsumed under another intention, such as performing a regular sunnah prayer.