An early warning then, Lucas will not change his name just because he's in Harry Potter's body. He will respond to others calling him Harry, but he self-identifies as the name given to him by his parents.

Not dropped, but I just had some important things going on. Planning to continue today.

He's not using it as world-wide travel though. He regularly takes a plane to go to far-away places like America or Saudi Arabia, and uses his Magic Carpet if he's not familiar enough with the area to be able to apparate. The max distance one can apparate is not just a few kilometers, and it's shown in universe he regularly apparates multiple times in a row to reach his destination. Regarding border control, if you want to operate in a legal manner, you need to register with the magical authorities, but there's no Anti-Apparition Jinx applied to the borders of all countries.

He is a wizard who can Apparate, so he isn't stuck in one place.

Yes, state-of-the-art for that time period.

He wasn't specifically searching for them. He wants to test the Resurrection Stone and needs some dark wizards to do it for him in case there is any magical influence. He doesn't want to get the test subjects from the UK, so he chose a random country—Russia in this case—and went to their magical hub. After waiting some time, he observed which dark wizards were the worst. He had already seen a couple, but after scanning their thoughts through Legilimency, he immediately chose these three for obvious reasons. Regarding his absence from school, you're correct that he can't stay away for too long. So he'll be away for a maximum of 2-3 hours before returning to Hogwarts.

He knows the melting points of various materials, which allows him to get a very good idea through that knowledge. That's also why he tested it with copper, steel, and granite—to establish some kind of baseline. After that, it's partly by feel/instinct, at least until he noticed the effects the heat had on the surrounding sand, air, and cliffs. That helped him pinpoint the temperature a little more accurately. But the temperatures being noted by him aren't 100% accurate; they will deviate slightly from what he is stating. It's not like his maximum with the artifact is exactly 5000 degrees Celsius, but it's near that amount.

Yes, I'm pretty sure that's why Rowling created Luna as a character. Though Lily Moon still exists independently of Luna in canon, even if she's only mentioned once in the first book.

Yes, but it's still his first official Herbology lesson at Hogwarts. It will take a little bit of time for him to see he's good at it.

Backup if something went wrong. He didn't need it, but it's good to be prepared.

These two are wary of him because he's been in Azkaban for so long that they think he must surely be completely insane by now. They don't know he's an Animagus. So because of that and the fact they are both not the most pleasant kind of people is why they are so rough with him.

All I'll say on this matter is that the Basilisk will not be left unused.

He's not stereotypically evil in the sense that he would hurt people for no reason, so he's more of a 'morally ambiguous protagonist' than a villain. Especially since he does have some good qualities, such as wanting to make the world a better place, even if it's for his own benefit in the future.

This is handled in the future.

It's more that Dumbledore doesn't know what spending centuries as a disembodied wraith can do to a person. Maybe Voldemort can gradually increase his strength even while a wraith? And who knows if that strength can accumulate over time? So, he is more afraid of the possibility that Voldemort can become much stronger.

It has only been three days since he arrived at Hogwarts, so he hasn't had time to explore the forbidden section yet. And there are more than enough books to go through in the normal section for now.

Yes, I meant more that Voldemort is now contained within the Ministry. I'll change 'capture' to 'containment' to make this clearer.

Oh, like that? I don't think they were particularly fearful of Voldemort in this chapter. They were dismayed that he is still alive, and Perenelle flinched once because she is sensitive to the lives lost because of him, but besides that, they were ready to help Dumbledore.

If it were the type of immortality that comes with eternal youth, I'd agree with you. However, with their decrepit bodies that can barely move, there's not much they can do. And if they were that powerful, they would have stopped Dark Lords like Grindelwald long before he became such a big threat, right? But that didn't happen, and Dumbledore had to defeat him. Similarly, if the Flamels were undefeatable, they could have dealt with Voldemort long before he terrorized the British Isles. They are indeed very skilled at Alchemy, Potions, and concealment magic, but that does not mean they are very skilled at battling with magic.

He develops this at a later point of time, since it's more efficient and subtle. But this is in the 'heat' of the moment, so he went with his first thought.