Incarnation of Arhat Ji Gong 濟公

For question #1, the Buddha addresses the death of arahants:

DN1:3.73.1: The Realized One’s body remains, but his attachment to rebirth has been cut off.
DN1:3.73.2: As long as his body remains he will be seen by gods and humans.
DN1:3.73.3: But when his body breaks up, after life has ended, gods and humans will see him no more.

Question #2 is about possession by a spirit. The Buddha discusses possession in at least four suttas. For example we have:

MN49:5.1: Then Māra the Wicked took possession of a member of Brahmā’s retinue and said this to me,
MN49:5.2: ‘Mendicant, mendicant! Don’t attack this one! Don’t attack this one! For this is Brahmā, the Great Brahmā, the Undefeated, the Champion, the Universal Seer, the Wielder of Power, the Lord God, the Maker, the Author, the First, the Begetter, the Controller, the Father of those who have been born and those yet to be born.

The Buddha responds to this possession quite firmly:

MN49:6.2: ‘I know you, Wicked One. Do not think,
MN49:6.3: “He does not know me.”
MN49:6.4: You are Māra the Wicked.
MN49:6.5: And Brahmā, Brahmā’s assembly, and Brahmā’s retinue have all fallen into your hands; they’re under your sway.
MN49:6.6: And you think,
MN49:6.7: “Maybe this one, too, has fallen into my hands; maybe he’s under my sway!”
MN49:6.8: But I haven’t fallen into your hands; I’m not under your sway.’

The other three suttas are also about possession by Māra and they also discourage possession. Please be careful--Māra has deceived gods.

"It is often the case in many Chinese schools of Mahayana Buddhism that an Arahant, although advanced in the path to enlightenment, has yet to reach Nirvana"
where is that stated ?

The only reference to that doctrine that I know of is from the Tibetan canon -- near the beginning of The Jewel Ornament of Liberation it says (I paraphrase), that there are five families:

1. Disconnected (immodest, no compassion, no thought for others, etc.)
2. Indefinite (may join one of the next three families, depending/conditioned on whether they make contact)
3. Hearer (fear samsara, yearn for nirvana, little compassion)
4. Solitary Realiser (like Hearer but also arrogant, keep their master's identity secret, solitary)
5. Mahayana

Hearers and Solitary Realisers engage in their respective vehicles and achieve the results of their practices, but this is not the final nirvana

If their states are not the final nirvana, then one might argue that the Buddha should not have taught these two paths. Is there a reason the Buddha should teach such paths? Yes. For example, suppose great merchants from this Jambudvipa are traveling the ocean searching for jewels. After many months at sea, in some desolate place, they become completely tired and exhausted and think, “There is no way to get the jewels now”. When they feel discouraged and prepare to turn back, the merchant captain manifests a huge island through his miracle power and lets all his followers rest there. After a few days, when they are fully rested and relaxed, the captain says, “We have not achieved our goal. Now we should go farther to get our jewels.”

Eventually they are awoken by the Buddha, cultivate bodhicitta, and

practice the bodhisattva’s path for many limitless kalpas and eventually achieve enlightenment.

It says you can find this doctrine also in the Gone to Lanka Sutra and in the White Lotus of Sublime Dharma Sutra.

These families (who haven't achieved "final nirvana") include Arhats -- towards the end it says,

The supreme worldly experiences—all the perfect powers, clairvoyance and meditative absorption, and so forth—are achieved through devotion to the Dharmakaya. Obscuration abandonment, clairvoyance, miracle powers, and so forth—all the qualities of Hearer Arhats—are achieved by slight realization of Dharmakaya. Obscuration abandonment, meditative absorption, clairvoyance, and so forth—all the qualities of Solitary Realiser Arhats—are achieved by partial realization of Dharmakaya. Obscuration abandonment, meditative absorption, clairvoyance, and so forth—all the qualities of bodhisattvas who attained bhumis—are achieved by greater realization of Dharmakaya.

See also Wikipedia Arhat: In Mahāyāna Buddhism.

The answer to this question may depend on the tradition.

In Theravada, the arhat is completely liberated and will never be reborn. The arhats and Buddhas are not supernaturally reachable after they have completed their Earthly lives. Also, trances and being mediums are considered wrong livelihood for monks.

On the other hand, I believe that in certain (if not most) Mahayana sub-schools, Arhats are not completely done in their path to complete enlightenment, and at some point will resume the journey. As high bhumi Bodhisattvas, they can be reborn, perhaps voluntarily. The same applies to Buddhas.

Also, in Tibetan Buddhism, trances and mediums are not uncommon. Certain oracles and Dharma Protectors can be channelled by mediums. For e.g. in this YouTube video, you can see the Dorje Shugden Oracle doing the Vajra dance, accepting offerings, providing blessings etc. This event was presided over, by the late Tsem Tulku Rinpoche.