I think its called a Bar-B-Que nowadays because the food was not wasted, it was eaten by the family. The meat prepared on the altar served the family in a practical manner, while the inedible parts of the "clean" animals were burned to ash. In the wanderings of Yah's children though the desert, this process was important because it eliminated dangerous waste which could bring disease and predators into their midst. The burning of inedible parts of 'clean' animals also served as a symbol, with the smoke rising up, being lifted up by the fire. This practice NEVER served to make anyone any more 'righteous' in the doing.
The word "sacrifice" in relation to Noah's(Bare'syth 8:20) and Abraham's(Bare'syth 12:8+) mizbeah(altar; a place to make offerings, platform associated with sacrifice) is misconstrued in the pegan bible. Confusion is easy here because people don't recognize how it is only a symbol, just like the menorah. The term 'mizbeah' is used quite often, especially in Qara/Called Out/Leviticus where it appears ~80 times. More to the point, the term is applied both to things that have pleased Yahowah, and to things which he hates (religion, religious worship).
In Mal'aky / Messenger / Malachi 1, we find an example of how an offering made on an alter(mizbeah) designed for Yahowah is found unacceptable, not because of the offering itself, but because of the misunderstanding of the individual making the offering. It is an example of how not understanding and observing the covenant and the relationship with Yah can cause a symbol to turn into a religious practice. Yahowah does NOT want sacrifices because he made the only one that really counts.
The simplest answer I could come up with in regards to your questions would be to not waste your time with trying to duplicate their actions, but instead try to learn from those actions and what they symbolize in relation to Yahowah, his towrah, and his beryth.
Copying action is a hallmark of religion. Observation and understanding are hallmarks of Yahowah's family.
To follow up on my BBQ comment, if you want to do something with food in relation to Yah, have a BBQ on a feast day. 'Que up some lamb burgers and remember what the lamb symbolizes. If you want, burn up the leftovers and ponder what they were doing in the desert and at the temple. Remember, its more about the observation of the symbols, not about the actions themselves.
Your 5th question could be answered rationally when you think of what an offering is; like sacrifices, offerings are highly symbolic. Offerings are made throughout the towrah, and in some places the offerings are rejected. The rejected offerings are almost always because the individual making the offering did not fully understand what the offering was in relation to Yahowah. They tried to make the offering to save themselves or for self gratification, possibly even to get attention. Those motivations don't please Yah.
The observation of the Shabbat really helps illuminate Yah's stance on the matter. In regards to his relationship, we are to set aside 1/7 of our time to rest and visit with him, NOT working to save ourselves. He is very clear about us not doing the work of the mala'kah (messenger, Ex: 20); we are not to try and save ourselves when we are with him.
Something else to remember is that most of the offerings and sacrifices mentioned in the towrah served as symbols in one way or another for the work done by Yahowsha the Ma'asehyah(implement doing the work of Yah). They performed these sacrifices and offerings because Yahowsha had not yet fulfilled the prophesies and the first four Mow'ed Miqra'ey(called out assemblies), Pesach, Matsah, Bikuwrym, and Shabuwa'. Today, we have Yahowsha's fulfillment to reflect on as the ultimate sacrifice and offering made by Yah. In that light, anything we could do would pale considerably. If you look at the Yahowsha's example, he never made an alter and his disciples never made offerings or sacrifices because they recognized that Yahowsha served as the ultimate offering from Yahowah to us. That is the key difference I see between those offerings made in the Towrah, and what we do today.
As for myself, I have not and will not build an alter in emulation of Noah because that would disregard Yahowah's instructions on how to do so in Exodus / Shemowth and Leviticus / Qara. His instructions in those places also include the Lowy / Uniter / Levites as assisting in the process, which unless you want to have Frank come out to help set it up, I don't think I know of another Lowy who in covenant and might be willing to help. The alters with the most explicit instructions in Qara were made in relation to the Temple, which has been destroyed as prophesy said it would, so thats not something we can accomplish at this time. When Yah returns, we can build a new temple, but with it comes an understanding of what it represents, which is NOT a place of worship as the religious believe. I practice as much of the Mowed Miqra'ey as I can with my family, observing as much of the symbolism as possible, but there are things I simply cannot do today. Among those things I consider alters, sacrifices and offerings as things I cannot do, along with bringing a lamb into my house before Pesach and slaughtering it with my family.
As for yourself and your family Nikolai, you are free to do whatever you please, but I urge you to closely examine and carefully consider Yahowah's dabarym (words) first, so as not to put the cart before the horse. I don't think Yahowah would be angry with you if you perform and offering and emulated Noah, Abraham, and Moseh in order to better understand what they did and how they did it, but before you attempt to duplicate their actions, attempt to duplicate their relationship with Yahowah. Understand why they built and alter and made an offering, and what those represent in relation to Yahowah before trying to do it yourself. Then its up to you. I'm not saying don't do it, I'm simply saying do your homework first.
I understand your desire to do something which would please Yahowah, and I know that the best example of that is in Dowd's life. Yes he did build and altar in 2 Sam 24, and he also composed music. The thing that I know which Dowd did better than anyone though, was understand and immerse himself in Yahowah's dabarym. It was though understanding Yahowah and his words that Dowd pleased Yahowah, the altar, offerings, songs, and poetry were byproducts. From his example I can be sure that we will be alright not building altars and making our own offerings, because the thing Yahowah values the most is our pursuit of him through his words. When Yah speaks of the fulfillment of Yom Kippurym, the key phrase he uses is yada' 'owty, which means that those estranged from him who are in the category of being descendants of Abraham and thus under the original covenant will become familiar with Yahowah, coming to respect and acknowledge Yah, and be known to him as he is known to them (paraphrase of Yirmayahuw / Jeremiah 31:34). In that passage Yahowah makes it clear that the relationship is incredibly accessible for all types of people, as long as they take the time and make the decision to yada(to recognise and aknowledge, to know and become known in a relational sense, to be aware and to be made aware, to teach and to be taught).