Gerund Phrases do not exist in Danish per se. In the sentence you provide, the gerund "playing" could be written in the infinitive form of the verb by adding "at" in front of the verb stem. Thus, the subject can be written as "At spille videospil med min søster" followed by "er sjovt" to complete the sentence. In other instances such at telling your friend through what you're doing right now, such as telling them "I'm cooking dinner", the most natural response would typically be something in the lines of "Jeg er ved at lave mad" or "Jeg er i gang med at lave mad", rather than simply saying "Jeg laver mad". By doing this, you more precisely convey that you're in the process of cooking dinner, as opposed to more vaguely saying "I cook dinner". As for your other sentences: 1a. Can drinking a cup of coffee a day protect you from cancer? Kan det at drikke en kop kaffe om dagen beskytte dig mod kræft? 1b. Drinking a cup of coffee a day can protect you from cancer. At drikke en kop kaffe om dagen, kan beskytte dig mod kræft. 2a. Can drinking a cup of coffee a day prevent you from getting cancer? Kan det at drikke en kop kaffe om dagen forhindre dig i at få kræft? 2b. Drinking a cup of coffee a day can prevent you from getting cancer. At drikke en kop kaffe om dagen, kan forhindre dig i at få kræft. Hope my answer helps. Please note that I'm merely a native speaker, not a linguist or qualified teacher of any sort.

1. How do you form gerund phrases in Danish? '-ing' in English is the same as '-ende' in Danish. Example: 'They called him the singing sailor'; "De kaldte ham den syngende sømand". Used adjectival, describing a noun. 2. "Playing video games with my sister is fun."; "Det er sjovt at spille videospil med min søster". We do not use gerund in a sentence like this one. 3. (1a+1b): 1a. Can drinking a cup of coffee a day protect you from cancer?; Kan en kop kaffe om dagen beskytte dig mod kræft? 1b. Drinking a cup of coffee a day can protect you from cancer.; En kop kaffe om dagen kan beskytte dig mod kræft. 4. (2a+2b): 2a. Can drinking a cup of coffee a day prevent you from getting cancer?; Kan en kop kaffe om dagen afholde dig fra at få kræft? 2b. Drinking a cup of coffee a day can prevent you from getting cancer.; En kop kaffe om dagen kan afholde dig fra at få kræft.