Should I practice a single mantra or multiple?

The implication in the question suggests that you have an inner inclination to recognize worldly suffering. From my experience, whilst this was a tough undertaking, it was a necessary part of my practice. I had been drawn to hold the world's suffering and not just at the planes of materiality but down into the collective human unconscious - literally going through the hell realms. In Zen terms this is called The Great Doubt. It had led to a great, unfounded compassion and an understanding of the suffering of others in all situations and at different levels.

I could go into more detail with that, but it would drown out the focus of this answer. Suffice to say, that one does not necessarily need to 'pain' themselves to such a degree, but that one makes a sign of recognition to the suffering of other beings in a way that is conducive to your current karmic structure. The thing about the karmic structure is that we cannot really know where our practice will take us; it is different for everyone. But there are universals that show themselves from time to time and that is why we have a context - like Buddhism - where other travellers who have fared the road leave clues, markers, and little signs written on scraps of cardboard.

I don't know anything about the seven-line prayer, but briefly scanning over it suggests that it promotes great reverence towards a particular guru. I was never drawn into salivating over teachers in this way. The point is to find your own reliance and not become hazed by someone else's idea of what a path is - no matter what robes they wear or what lineages they bonk you on the head with. These things are only fluff sprinkled with glitter.

Now, ask yourself: is it sincerely possible to focus your efforts onto a single practice with the goal of stream-entry?... No! No! No...

The Japanese Zen Master, Hakuin, points this out with succinct beauty:

“People see it as if it is far away. What a pity! They are like a man who, standing in water, complains of thirst”

The supposed supernatural benefits of mantras are questionable, in my opinion. Mantras are a learning device to help fix the mind on a single area of concentration. All of the most profound mantras are mostly silent. They are contenplative strings of meanings assigned to non-semantic or semantic syllables.

I mean, perhaps "oṃ bhaiṣajye bhaiṣajye mahābhaiṣajya samudgate svāhā" can cure an illness, but personally I have no faith in the material medicinal benefit in chanting these words. IMO, and as I have been taught in the esoteric teachings I have received in the past, the mantra is a pedagogical device for leading the mind towards liberation, not for transforming the physical maladies that plague the physical body and the world it is in. That being said, in the texts that transmit these mantras as well as in the living traditions that do so, supernatural, supernormal, and/or magical benefits are supposed to accompany their usage. I won't say that there's no such thing as a seemingly-miraculous event caused by a mantric recitation, but I've certainly never witnessed such a thing with my own person.

If you've taken formal refuge with a Tāntrika guru, if you practice the guruyoga, only your guru can answer this question. In a Vajrayāna context, there is nothing wrong with reciting a mantra or dharani that does not require a specific ordination/empowerment. The Medicine Buddha mantra requires no ordination or empowerment. Similarly, the Prajñā mantra (i.e. "gate gate" etc.) requires no initiation or empowerment. Ask your guru if the mantras you are attracted to require specific initiations ("lung" in Tibetan).

If your goal is stream entry, then you need to break the first three fetters. These fetters are (in no particular order):

• Self-view: the state in which clinging to the five aggregates creates a sense of self — an 'I', 'me', or 'mine' — that appears as permanent or irreducible
• Rites and Rituals: the state in which practices or doctrine are treated as though they have power in themselves to create attainment, regardless of one's understanding
• Blind Skepticism: the state in which intellectual theories and arguments are allowed to outweigh and supplant experience

Mantras have their uses, but they fall too easily into the 'Rites and Rituals' category. The ideal of a mantra is to embody the spirit of the mantra, but far too many people repeat mantras endlessly, without ever grasping the real essence of them. That is of no use.

With all that in mind, well... Make a choice and commit to it. If you choose to stay with one mantra, stay with it, and dive into it. If you choose to experiment, experiment fully and diligently. Know in your heart that whichever path you chose you will eventually have to abandon. The mantra — if it's well-given, and well-designed — is there to break a fetter, and once the fetter is gone the mantra will be pointless. Then you will move on to other, higher, better practices (which you will also ultimately have to abandon).

Sigh...

Stream entry means leaving the sure footing of the dry earth of common understanding and giving yourself to the waters of potential. No one does it unless they throw themselves (calmly and confidently) into it. But the commitment isn't to the waves; the commitment is to the far shore. Understanding that distinction is what one must focus on.

From my experience of Tibetan Buddhism, you probably need an empowerment for each mantra. Empowerments are effectively introductions.