What is the actual status of the Dalai Lama in regard of Dhamma-Vinaya?

This says that the Dalai Lama is ordained according to the Mulasarvastivada Vinaya:

His Holiness the Dalai Lama Bestows Ordination Vows

Today, His Holiness the Dalai Lama gave a group of monks full ordination according to the Mulasarvastivada Vinaya tradition that was established in Tibet by the Indian Abbot Shantarakshita in the eighth century CE at the behest of the Tibetan Emperor Trisong Deutsan.

Prior to the ordination His Holiness and the senior Bhikshus who assisted him performed the ceremony of confession and restoration, confessing and purifying any infractions of their own vows in preparation for granting the ordination to others.

Wikipedia says,

The Mūlasarvāstivāda was one of the early Buddhist schools of India. The origins of the Mūlasarvāstivāda and their relationship to the Sarvāstivāda sect still remain largely unknown, although various theories exist.

The continuity of the Mūlasarvāstivāda monastic order remains in Tibetan Buddhism, although until recently, only Mūlasarvāstivādin bhikṣus (monks) existed: the bhikṣuṇī order had never been introduced.

Vinaya lineage

The Mūlasarvāstivāda vinaya is one of three surviving vinaya lineages, along with the Dharmaguptaka and Theravāda. The Tibetan Emperor Ralpacan restricted Buddhist ordination to the Mūlasarvāstivādin vinaya. As Mongolian Buddhism was introduced from Tibet, Mongolian ordination follows this rule as well.

The Mūlasarvāstivāda Vinaya is extant in Tibetan (9th century translation) and Chinese (8th century translation), and to some extent in the original Sanskrit.

When I researched this answer I remember reading of some people who claimed to be Tibetan Buddhist teachers, who were told they weren't welcome to visit the Dalai Lama because they weren't living according to the Vinaya (e.g. they were known to be associating with women).

There's also this article:

Meeting Delegates to the Second Dialogue on Vinaya

This morning His Holiness the Dalai Lama met with delegates who had participated in a Second Dialogue on Vinaya. They included representatives of the Sri Lankan, Burmese, Thai, Vietnamese, Taiwanese, Indian and Tibetan Buddhist Traditions. Among reports read to the gathering was one from a senior Elder of the Thai Forest Monk’s tradition, who approved of the spirit of the meeting, but expressed regret that since proceedings were being held in a hotel it was inappropriate for him as a Forest Monk to attend. Nevertheless, he encouraged delegates by quoting the Buddha’s having told Ananda that after his passing away, the Vinaya would be the disciples’ guide. He added that as long as the Vinaya prevailed, the Buddha’s teachings would survive.

Further reports clarified that in their discussions delegates had recognised that although the various Vinaya traditions may vary in the numbers of specific precepts, they shared the seven fundamental divisions of the Vinaya. There are proposals for further such dialogues to be held.

His Holiness opened his remarks by declaring his own status:

“I am a Bhikshu, who received full ordination in 1954, and I belong to the Nalanda Tradition that was introduced to Tibet from India in the 8th century. The person primarily responsible for this was Shantarakshita, one of the foremost scholars of Nalanda University, a Bhikshu, philosopher and logician. He was invited by the Tibetan Emperor. The Nalanda Tradition places great emphasis on the use of reason over mere faith.

The 14th Dalai Lama has no standing in the Theravada Buddhist tradition.

However, in the Tibetan Mahayana Buddhist tradition and conforming to the Dharma and Vinaya of Tibetan Buddhism (and in particular, the Gelug school), the 14th Dalai Lama Tenzin Gyatso is:

• a Tibetan Buddhist monk
• a Tibetan Buddhist lama i.e. a teacher of the Dharma (as taught in Tibetan Buddhism)
• a tulku (reincarnate custodian of a specific lineage of teachings)
• incarnation of Bodhisattva Avalokiteśvara
• head of the Gelug ("Yellow Hat") school of Tibetan Buddhism

The bodhisattva's achievements in Mahayana Buddhism is measured in bhumi levels. However, it's unclear to me what is the bhumi level of Bodhisattva Avalokiteśvara.