Learn Turkish: Yeni yazılım her gün veri indirir. - The new software downloads data every day.

The verb root is indir- (to download or lower). For verb roots with more than one syllable that end in a consonant, the aorist suffix is -Ir (which can be -ır, -ir, -ur, or -ür). Since the last vowel in indir- is 'i', we use -ir to match, giving us indirir.

Could I use the present continuous tense and say indiriyor instead?

You could, and you will hear native speakers use -iyor for routines too. However, the aorist tense (-ir) is the best choice here because of her gün (every day). The aorist is specifically used for habits, general facts, and regular routines, just like the simple present tense in English.

Why doesn't veri (data) have an accusative suffix (like veriyi)?

Because the software is downloading data in general, not specific data (the data). In Turkish, when a direct object is non-specific or indefinite, it doesn't take the accusative case marker and usually sits right in front of the verb.

Do the words yazılım (software) and veri (data) come from verbs?