It would really be helpful to try to list as many details as you can for each individual story together as a group, and to review the guide that I mentioned to see what other details might be drawn from your memory. This forum is pretty good at finding specific stories, but the trick is often to find little details that overlap with other people's memories. Sometimes two or three small details together is enough to get others who half-remember the same story to ask more questions or contribute their own details.
To review:
1. This is a single collection that you are looking for. Can you recall anything about the cover? How thick it was? The overarching theme of the collection? When and where you read it? The names of any authors or stories that you remember as being in the same collection?
2. The first specific story that you remember from this collection involves a man getting his arm stuck in an "eldritch portal" and being shot by a colleague. The main character and his colleague were associated via a college or university, possibly located in England or Great Britain. Were they both men? Both professors? Both students? A professor and a student? Any details of the college or university that you can recall? Were they in the same department? Which department? A "portal" implies a passage to somewhere -- what was on the other side? "Eldritch" implies magic -- was this portal created by magic or by technology? Can you remember anything about the method by which it was created? Why did his arm get stuck? Was it his whole arm or his hand or what? Why did his colleague shoot him? Was it to end his misery, to ensure the portal closed, because the colleague was possessed or similar?
3. The second specific story that you remember involves a girl walking her dog in the park and "getting an alien parasite." The dog died partway through the story, and this event was "integral" to the plot in your opinion. How old was the girl? Where did she live? What kind of dog did she have? Was this on Earth? What time period? How did the parasite get to the park? What did it look like? What was the effect of the parasite on the girl? Was she in danger? Was the parasite removed? If so, how? What did the dog do that was significant? In what way as the dog's death important to the plot? Did the parasite kill the dog? If not, how did the dog die? Were there more parasites than the one affecting the girl? Were the parasites intelligent? Did the story end on a good note or a bad note?
4. The third specific story that you remember involves a man pushing a baby stroller in the rain and a "hitman(?)" coming to talk to him. The hitman shoots the man pushing the stroller and departs with the stroller. What was in the stroller -- a baby or something else? If it was a baby, why was the man pushing it in the rain? Did the hitman specifically come to get the contents of the stroller? Did the man know why the hitman was coming? If not, did the hitman explain? Was the hitman working for an organization like a government, corporation, or secret society? Did the man recognize the hitman or was he caught by surprise?