Learn Russian: Я открываю окно.

Because окно is a neuter noun. When an inanimate noun is masculine or neuter, its Accusative form (used for direct objects) looks exactly like its Nominative (dictionary) form. You only need to learn new endings for feminine nouns in this case.

Is открываю a special continuous verb form since it translates to "am opening"?

No, Russian only has one present tense. The single verb открываю covers both "I open" (as a habit) and "I am opening" (right now). You rely on the context of the conversation to know which English translation fits best.

What is the dictionary form of открываю?

The dictionary form (infinitive) is открывать. Since the subject is Я (I), the verb takes the first-person singular ending. For this regular verb group, you remove the -ть from the infinitive and add -ю.

Why does the first letter in окно sound like an "a" instead of an "o" when spoken?

This happens because of a very common Russian pronunciation rule called vowel reduction. The stress in the word окно falls on the second syllable. Whenever the letter о is unstressed, it is pronounced like a short "a".