Learn Farsi: با پیپت دوازده ممیز پنج میلی‌لیتر آب اضافه کنید. - Add 12.5 milliliters of water with a pipette.

Yes. Even though it is not written, you pronounce an ezafe right after momayyez, reading this as davazdah momayyez-e panj. The ezafe acts as a link between the word for decimal and the number that follows it.

Why isn't there an ezafe between میلی‌لیتر and آب to express milliliters of water?

In Farsi, when you specify a quantity using a unit of measurement, you do not use an ezafe to connect the unit to the noun. It is simply mili-litr ab (milliliter water), similar to how you would say yek kilo sib (one kilo apples) without an ezafe.

Since 12.5 means twelve and a half, could I substitute the decimal with دوازده و نیم?

You could in casual conversation, but in this context, it is better not to. Because this sentence is an instruction using a precise scientific tool like a پیپت (pipette), it is much more natural to state the exact decimal value using momayyez rather than the everyday word for a half, nim.

If I wanted to expand this sentence and specify adding the water to a test tube, what preposition would I use with اضافه کنید?

The compound verb اضافه کردن (to add) uses the preposition به (to) to indicate the destination. You would use it right before the destination, creating a phrase like (to the test tube) earlier in the sentence.