I'm a native American English speaker and I can't tell if it's a British or American accent. That's funny.

1. "took" because the 19th century and the renovations were in the past so you need to use the past tense version of the verb not "take" which is present 2.Hot dogs are the best American style 3."To" or "through" depends on weather you actually can go inside and tour the castles and other things. If you can it's "through", if not then I would say "to" but it's really kind of interchangeable. I would use "near" in this case, it would sound weird to a native speaker if you use "nearby". 4. "after rain"

That sentence and the use of 'the name' is correct.

All of these sentences are right and commonly heard however when you would use them would depend on context. Like for the first one someone might say they need the dishes done and you can say 'I got it' meaning you'll do them. For the second one, you might be playing a sport and want to make it clear you're going to get the ball you would say 'I've got it'. For the third one, someone could be explaining something to you that you already understand so you could say 'I get it'. The last two are really interchangeable in most cases. Of course, the examples I gave aren't set in concrete and the first 2 sentences are really interchangeable too mostly and if you make the third sentence 'I will get it' it can be used instead of the first two in some situations too. All the sentences are correct, you learn to use each one with practice in context.

Those are all correct and commonly used.