Does the Maha Parinirvana Sutra acknowledge the existence of eternal spirit/soul?

The core practise of anapanasati is defined as follows:

"the monk on that occasion remains...ardent, alert & mindful — putting aside greed (liking) & distress (disliking) with reference to the world."

Therefore, giving up positive & negative judgments does not require giving up belief in a 'self', 'soul' or 'aatman'.

Just make the mind non-judgmental & let it naturally connect with the breathing. When anapanasati has been well-developed like this, the mind will eventually become deeply peaceful, radiant, concentrated & free (and in this deep samadhi, insight into anatta may occur, naturally, by itself).

Buddhism is not about 'belief' or 'blind faith', including blind faith in 'anatta'. The Buddha taught the path begins with giving up craving, which is the condition for samadhi to develop.

The Buddha taught:

For a person whose mind is concentrated, there is no need for an act of will, 'May I know & see things as they actually are.' It is in the nature of things that a person whose mind is concentrated knows & sees things as they actually are.

Cetana Sutta

I don't think that that would be considered a valid interpretation because selflessness is one of the three marks of existence and therefore stating that any phenomenon had an enduring self-nature would be something to investigate more deeply and with an open-mind.

That said, we all have Buddha Nature, which is precisely what the maha pari nirvana sutras speak of because sentience in its most natural and un-inhibited form is actually pure enlightened nature in manifestation and pure manifestation in nature. it is not something that is easily understood because it completely challenges the entire notion of a separate self that is the benefactor of our experiences.

that is to say, it is not that we lack autonomy -- we have the ability to steer our ship, and as it is stated in many places with epithets such as "mind over matter" or in the opening verses of the Dhammapada, the mind is the king. Mind is the fore-runner of all phenomena. In this way, we can talk about an "enduring substance" but it would be folly to assume that we could actually "grasp" onto it or hold it still for a second, because this is actually the Experience and not the Object of experience, as it were.

So consider that we all have Buddha Nature, that there are countless Buddhas actually walking around among us, and that our whole experience is actually a continuous process of enlightenment, however it is very important to share knowlege, honor teachers, and grow together because this trip is far more far out than any individual aspect could understand, so in short I simply want to add that mind is indestructible and continues forever, however it is not a "soul" because a soul would have some sort of limitations obscuring omniscience. Buddha Nature is the uninhibited mind in manifestation and can only be realized through a mind founded upon the notion of renunciation, because belief (firm belief) in the notion of an enduring existence or situation is precisely what causes the evolving cosmos cramps. "They are growing pains" is something some zen masters say, and knowing life situations in this way can be truly helpful and liberating.

So during anapanasati meditation, the whole focus is the breathing, single-pointed focus on the rhythm of breathing, it's a dynamic flowing event stream, so try and stick with it. Ideally you start with a support, and the breath is wonderful because the breath is nonconceptual -- it is something you can directly feel and experience without labeling it that or this.

Please ask any questions, I am happy to share what I have learned so far on this path. May this help.

The second part in the posting below attempts to give an answer to your question stated in the title; the second question I can only comment with subjective view in the first part

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1) I think there is no "restriction" or prerequisite (like for instance a system of permits) for mindfulness-meditation. Just try and see how far you come.

However, the Buddha said, (and it is quite reasonable for me) that for the full liberation from the attachments to emotions and mental figurations, and for the true emancipation from (and eradication of) tanha , the illusion of an inherent, eternal, unchangeable Self atma has necessarily to be dissolved.

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2) I copy&paste some excerpt from the Mahayana-Mahaparinirvana-Sutra (taken from links found at Dr. Tony Page's site). The following are the last couple of paragraphs from the third chapter.
I find it a bit strange to say the least, for instance that a man like we know it as the Buddha from the palicanon comes to be a doctor to "subdue the tirthikas" ...

If I understand that excerpt correctly, then it is suggested, that the concept of no-self, of "an-atman" is only teached in the framework of concurrence of the "doctors" and "... because of this,(...)" and it is continued, that it had also been said, that there is a self, namely "... it is not that they [the dharma/the phenomena] are completely devoid of a self".

The text is suggesting, that the Buddha did not teach the non-existence of the self simply because of the non-existence (what would be the natural assumption) but because of didactical reasons (and actually means something else)!

Below now the excerpt, emphasis added by me: source

Chapter 3
(... final paragraphs)

"Know, O you Bhiksus!

The same is the case with the Tathagata, the Alms-deserving, the All-Enlightened-One, the Unsurpassed Best Trainer, the Teacher-of-Heaven-and-Earth, the Buddha-World-Honoured One. He comes as a great Doctor and subdues all tirthikas and bad doctors. In the presence of kings and all people, he says: "I shall become the King of doctors and subdue tirthikas."

Thus we say: "There is no self, no man, no being, no life, no nurturing, no knowing, none that does, and none that receives."

O Bhiksus! Know that what the tirthikas say is like the case of a worm that eats upon [a pie-ce of] wood, from which, by chance, there appears what looks like a letter.

Because of this , the Tathagata teaches and says no-self.

This is to adjust beings and because he is aware of the occasion. Such non-self is, as occasion arises, spoken of, and it is [also] said that there is the Self.

This is as in the case of the learned Doctor, who knows well the medicinal and non-medicinal qualities of milk. It is not as with common mortals, who might measure the size of their own self. Common mortals and the ignorant may measure the size of their own self and say, 'It is like the size of a thumb, like a mustard seed, or like the size of a mote.'

When the Tathagata speaks of Self, in no case are things thus.

That is why he says:

'All things have no Self.'

Even though he has said that all phenomena [dharmas] are devoid of the Self, it is not that they are completely/ truly devoid of the Self.

What is this Self? Any phenomenon [dharma] that is true [satya], real [tattva], eternal [ni-tya], sovereign/ autonomous/ self-governing [aisvarya], and whose ground/ foundation is un-changing [asraya-aviparinama], is termed 'the Self' [atman].

This is as in the case of the great Doctor who well understands the milk medicine.

The same is the case with the Tathagata.

For the sake of beings, he says "there is the Self in all things"

O you the four classes! Learn Dharma thus!"