"Stalk" generally means to follow someone around, keeping track of their daily activities and what they do, where they live. It is usually done without their knowledge. "Cyberstalking" is doing this on the internet. For example, looking through many years' of someone's old pictures on Facebook, obsessively checking where they are, etc. So the sentence "cyberstalking from the comfort of our phones" means that people can "stalk" someone without ever having to leave their house. It is talking about the dangers of technology. A significant other is your spouse/boyfriend/girlfriend/partner etc. So being without a significant other means being single :)

It's a play on words. The normal expression is "From the comfort of our homes" means to do things in comfort from home. without even having to go out. "From the comfort of out phones" similarly just indicates that it is easy, you do not need to do anything difficult.

Cyberstalking would mean stalking, obsessively tracking what someone else is doing, saying, or where they are going, but through the internet. I would guess the first sentence implies that because of technology, it is now far simpler and easier for people to engage in this type of behavior without the discomfort or difficulty they may have faced before, when they would have been forced to follow people in person. "Significant other" is a term for a boyfriend/girlfriend, spouse, or lover, without being specific about the sex of that person or the level of the relationship. It's used sometimes when people don't want someone else to know details of their personal relationships, or as it would seem in this case, because it applies broadly to all romantic relationships. The study found that when people think about being alone, they are not as smart as they normally are, at least for a moment. Different examples for each: "It is easy to criticize an athlete from the comfort of your living room." "The politicians were making decisions about the war from the comfort of their offices back home." "I don't find it strange, but my significant other really dislikes when couples sit on the same side of the table, instead of across from each other, in a restaurant." "Mike's significant other is an excellent poker player."