How could the Buddha have been on this Earth as an Arahant if Arahants[-To-Be] can only be reborn in a higher plane (A Heavenly plane) of existences as according to the 4 Stages of Enlightenment?
The earliest scriptures depict a 'hearer' (such as Kondanna or Upatissa/Sariputta) attaining stream-entry and soon after attaining Arahantship.
The one or two suttas (such as AN 3.87) that more strongly infer a stream-enterer has at most seven more lifetimes appear to be illogical; given they infer a "same self", which is contrary to the stream-enterers destruction of "sakkaya ditthi" ("view of real self"). For me, these suttas appear to be later Abhidhamma, inputed into the suttas.
The most well-known sutta about stream-entry, namely, SN 13.1, is often falsely translated as including the phrase "seven more lifetimes at most" but the Pali actually does not include the words "lifetimes". SN 13.1 appears to say a stream-enterer has "seven more fetters at most to breakthrough".
Also, the phrase below about Non-Returners might also be questionable in its translations and interpretations. For example, two different translations and interpretations below:
Santi, bhikkhave, bhikkhū imasmiṃ bhikkhusaṃghe pañcannaṃ orambhāgiyānaṃ saṃyojanānaṃ parikkhayā opapātikā tattha parinibbāyino anāvattidhammā tasmā lokā—
In this Saṅgha there are mendicants who, with the ending of the five lower fetters are reborn spontaneously. They are extinguished there, and are not liable to return from that world.
Bhikkhus, living in this community there are bhikkhus who are Non-Returners through having ended the five lower fetters, who are spontaneously arisen,7 who will realize perfect coolness in that existence and by nature will never return from that world. Bhikkhus such as these are living in this community of bhikkhus.
7. Oppatika, born instantly and fully mature without going through the process of conception, gestation, infancy, and childhood-that is, instantaneous mental birth (not necessarily "re-birth").
Also the suttas (eg. MN 123) about the Bodhisatta coming to earth from heaven seem mythological because in these suttas the Baby Bodhisatta walks and talks about 'himself' from childbirth, which is contrary to suttas such as MN 64, which say a new born child has no conceptions of self.
Is using items within the same familial household without permission (such as a pencil, laptop, or a clothing item from a brothers room) considered a breach of the 2nd Precept?
If there is an explicit understanding in the family these items are to be used for the whole family then it does not break the precept. But, yes, if you take your brother's things without permission, it is a breach of the precept. The precept is for the purpose of developing respect for the property & feelings of others.
How is (with all respect) Venerable Yuttadhammo Bhikkhu able to be in the presence of a nun or the nun in his presence if it breaks the monastic rules?
Many of the Vinaya rules are about monks avoiding giving bad impressions to laypeople. Without knowing the specific rules exactly, in my opinion, there is a breach of the Vinaya because the videos looks like the monk & nun are together in a private place. Also, their posture & dress looks sloppy & undisciplined. Undisciplined looking monks & nuns will only attract similar undisciplined people to Buddhism, which is pointless when these converts cannot practise Buddhism due to their sexual obsessions and lack of sexual boundaries. Keep in mind sexual desire is the 1st hindrance to entering the Noble Path.
How do monks and nuns get their Tipitaka materials, monastic dwellings, and other worldly things while at the same time not being involved with any medium of exchange? Do they ask lay people to do so? Wouldn’t that be requesting for something, which I’m assuming is prohibited too in terms that they accept & don’t request for thing?
Lay people offer them. If lay people don't understand, I imagine the monk explains. For example, if a monk is on alms round in a non-Buddhist country, people, out of curiosity, will ask the monk: "What are you? What are you doing?". I imagine the monk would reply: "I am a Buddhist monk. I have vows of not using money. I go on alms round to collect food to feed myself for my spiritual practise. I place my trust & faith in the goodness of people to offer me food. In return, I teach them Dhamma, if they ask".
This famously happened to Ajahn Sumedho in England, who was offered land for a monastery by a non-Buddhist stranger. Read below:
In the spring of 1978, one of those small miracles happened that stop the mind's rational expectations. Keeping to the apparently pointless routine of going out for alms every day, as prescribed by Ajahn Chah, Ajahn Sumedho encountered a lone jogger on Hampstead Heath whose attention was arrested by the bhikkhus' appearance. This jogger had acquired an overgrown forest in West Sussex called Hammer Wood, out of the wish to restore it to its former glory – but he also understood that this was work for more than one man and one lifetime. Although not a Buddhist, he had the openness of mind to appreciate that an order of forest monks might be the perfect wardens for his woodland. Subsequently, he attended one of the ten-day meditation retreats that Ajahn Sumedho held at the Oaken Holt Buddhist Centre near Oxford, and later made an outright gift of the forest to the Sangha. This marvellous act of generosity...
How The Buddha Came to Sussex