TL;DR : There are many "rule" like posts among the guidelines which are not to be discarded or ignored as a whole while taking a decision on per site metas.
Highly upvoted answers of this site are not only cited on Hinduism meta but on other per site metas as well.
The reason users cite it is Meta Stack Exchange is a meta-discussion of the Stack Exchange family of Q&A websites. So, users from all the sites take part in it. It is called as mother meta and all other sites are child metas. But this is not the only reason it is cited.
It has been around for a long time and there had been many constructive discussions. So, it is possible to find an appropriate solution from already discussed question. When a situation arises, we obviously look back into the past on what others did to face the situation. In the same way, when a similar situation occurs on a per site meta, it is natural that a post from this site is cited as an example. Help will be given at
Hogwarts Meta Stack Exchange to those who ask for it (properly).
The community manager team are more active on the site and write posts regularly than other meta sites. So, posts on this site are more likely to get an answer from the official source i.e., CM or developers. Changes of policies, rules, guidelines are discussed here. So, these posts carry more weight as sources on other site metas too.
Users are not from only one site. Inputs from different users are given here. So, there is a scope of more useful and helpful discussion. (This post is a live example because you already got answers from two diamond moderators of other SE communities). So, highly upvoted answers are applicable to child metas most of the time.
In some posts here, useful posts of child metas are also cited here. It depends on the usefulness of the post and how much it is applicable to the situation faced on other metas.
For your first question,
Apart from faq, help center and answers from official sources like direct answers from community managers team, many meta posts can be considered as rules and followed not because just of votes, but due to the content and solution applicable to the situation we are facing. e.g : This post about chatty comments can be applied across the network.
This post can be followed too.
There are topics where MSE posts can/should be followed without any doubt like canonical posts like Not an answer, when to flag comments, closing questions as duplicates etc.,
There are some situations, where the decision should be taken based on site specific meta decisions. So, meta posts do not matter much there except for reference.
We cannot guarantee accepted answers as guidelines because in some cases, OP accepts the answer he likes rather than giving more useful information.
Highly upvoted answers can/should be followed based on the useful information it provides.
For your second question,
All the rules are not given in the help center. For example, the privileges page says about approval of tag wikis. But it is not explained what process is to be apply to review wikis and excerpts. The guidance given is not very much useful. In this situation, the relevant meta post becomes important. They should be followed just like rules. Same applies to all the review queues. So, we can't just say meta posts are not rules. There are also guidelines which are not to be discarded while participating on other sites. It is a mix up.
It is enough to be clear with the help center and faq of respective sites (what is on-topic and off-topic to ask. Policies they follow which are derived after a constructive discussion like comment policy, spoiler policy). Here meta SE does not play any role. Child meta does). But when a situation comes, it would be very helpful to know the guidelines of Meta Stack Exchange also. It is almost not possible to know each and every post of MSE as there are thousands of them already (That is the reason users from other sites refer MSE).