So, there is some legitimate controversy here, but it isn't a slam dunk case for assassination.

The specifics go something like this, for your points.

1. Stalin's guards were always ordered to stay outside his room. This was his own order, and I don't think has anything to do with assassination or not.

2. This is the argument of a guy named Faira who wrote an analysis of Stalin's autopsy a few years back. I had heard about it, but this thread prompted me to go and read it in full. It is fairly brief. He essentially concludes that the symptoms, particularly internal bleeding in several organs, are what you would expect from a dose of something called warfarin. I'm not a doctor, so I can't really contest that conclusion. However, it really isn't a historical argument, and the entire article has something like 8-10 sources. It's interesting and worth thinking about, but not an open and shut case in my opinion as a historical argument.

3. Montefore's Court of the Red Tsar is where I think this claim is most prominently featured. Overall the book isn't a terrible biography of Stalin, although I don't think it's the best out there. It is a trade book and therefore not published through an academic press, although it is generally well researched. Beria certainly didn't seem to lament Stalin's death, but then, many didn't. I doubt his statements would hold up in a court of law as evidence he killed him.

So, there are a few options here:

1. Stalin died of a stroke and brain hemorrhage. Doctors tried to save him, but the damage was lethal and they couldn't do anything about it. Pretty much the "official" story. This seems entirely plausible to me. People in their 70s sometimes have a stroke that kills them, especially if they aren't treated immediately, as Stalin wasn't.

2. Stalin had a natural stroke, but doctors botched his treatment, and this ended up being the decisive factor. Also possible.

3. The same as 2, but the doctors were compelled to mistreat him or their treatment was sabotaged. This seems slightly more likely to me than a straight up poisoning. It is also a little more consistent with Beria's statements, depending on how you read them. It seems to me there wold be more evidence of this if it were true.

4. Stalin was poisoned, causing him to have a stroke that eventually killed him. This one can be combined with any of the above possibilities for treatment or lack there of.

My feeling is that something close to the official story is close to right. Most of the accusations in foul play seem to be based on circumstantial evidence or require a leap that as a historian I'm hesitant to make. It's not impossible that there is more to it, but I'm mostly unconvinced at this point. So to answer your question as asked there are some things surrounding Stalin's death that can be taken as evidence that there was foul play involved, but nothing so clear cut that I think it can be taken for granted.

There are a few reasons the story is enticing though: First,I suspect that kind of eternal image of Stalin in his 50s that was reproduced for countless amounts of propaganda plays into the idea that he was poisoned because we imagine Stalin was younger than he was at the end, and in perfect, radiant health. But he was getting old, 74 to be exact, and had even thrown out the idea of stepping down from the position of General Secretary at the 19th Party Congress which was held about 5 months prior to his death. He cited his age as the reason at the time. Second, Stalin did a lot of things that you can imagine people would want to kill him for. It makes it a lot easier to accept that he was assassinated because it isn't a stretch at all to think that Beria (or someone else) would want him dead. But this isn't evidence enough on it's own to make an argument for assassination either.