Reminder, the Ho Yay is defined by being homoerotic.

>Madoka x Mami

Mami was more "taken" with Madoka because she had an extremely high karmic destiny, thus could be a powerful magic girl, this is not a romantic attraction.

The YouAreNotAlone speech scene, Mami is happy about it because she had been alone for many years and she finally found someone she could share her burden with. It is not romantic.

Being on a team does not indicate romantic attraction.

The max relationship scene for them is Mami about to say that she is her friend/family. It's call back to a similar line Mami says about Kyouko when they said they were sisters.

>Kyouko x Mami

First off, Farewell Story and TDS are not canon. They are not written by anyone who has anything to do with the main canon anime production. There is also no story narrative in the main canon which acknowledges the events in Farewell Story and TDS actually happened in the same setting.

Kyouko and Mami specifically say they are like sisters. And Mami treats Kyouko like she treats all of the other girls in the series, expect for Homura.

This "double message" is based on a mistranslation. The Japanese word for girl friend and and friend are totally different. The "double meaning" only comes when you remove that context in English. Tomodachi, meaning friend is the word used in that line. The word "koibito" means girlfriend. Here's a hint, just because some random anonymous post says it's correct doesn't mean it is.

Kyouko likes to eat, Mami gives her free food. This is not romantic attraction.

Kyouko didn't die with Sayaka in that time line because she was trying to find a way to save her after the fact.

>Mami x Sayaka

See previous point about how TDS is not canon. Reminder, official and canon do not mean the same thing.
Also, I'm not sure how that whole first line is suppose to imply homosexual attraction.

Saving your friend from death doesn't mean you are romantically attracted to them.

Is that scene Mami was trying to save herself more than anything. This same thing also holds true later when Mami tries to kill herself with Sayaka. It's only for the sake of trying to make herself feel better, which Homura caught on to right away and why she slapped her.

As for the familiars, Sayaka and Kyouko were her only actual friends.

>Madoka x Sayaka

They are close, but it is pure friendship. The whole time they are together in this "ho yay" situation, they are both aware that Sayaka is romantically attracted to Kyousuke.

The next entree even says itself it's a joke.

The misunderstanding is a joke Hitomi was trying to make. At the time Hitomi goes "both girls!!!!" she was already aware that Sayaka was in love with Kyousuke. As she confronts her about it soon after.

TDS still is not canon, and again, saving your friend is not romantic.

>Kyouko x Madoka

The only thing listed here is actually evidence of Kyouko x Sayaka, not Kyouko x Madoka. The only reason Kyouko interacted with Madoka in the first place was to find a way to save Sayaka.
Also, Kyouko, the old her, was normally protective and wanted to save her. At the point she starts interacting with Madoka, she was being close to her old self, so it's only normal she would defend Madoka who was a normal girl at the time.

>Homura x Sayaka
Putting your faces close together has nothing to do with romantic attraction. See https://puu.sh/vdcx5/a8551fc094.png

>Homura x Kyouko

She only considers working with Kyouko because she is the most grounded and sane one out of them.

>Mami x Homura

Mami's weapon is ribbons, of course she is going to attack people with them.

>Relevant information folder

Ume Aoki has nothing to do with TDS, this information under her name doesn't make sense.
And the "infinite possibilities" that is talking about is about their teacher and student roles. The person is misquoting the author's afterword.