I'm honestly not super familiar with わざわざ so I can't say for sure. I think it mostly means "purposefully" or "intentionally", so I guess it makes sense. But the first part of your sentence doesn't seem grammatically correct.
I don't think ~たい form and ために are used together. So I'd rewrite that as:
エッフェル・タワー見たいから、わざわざとパリに来た。(That's assuming you haven't seen the Eiffel Tower yet; if you already have, then I'd say "見たかったから".)
Or you could say:
エッフェル・タワーを見るために、わざわざとパリに来た。
But I have a feeling that a native speaker wouldn't use わざわざ in this kind of sentence.
It doesn't work that way in English either. If your sentence is translated literally into English, it would probably be "In order to want to see the Eiffel Tower, I went all the way to Paris." I can check my grammar book sometime and see what kind of verbs forms can be used with ために if you want. :)
I am not sure where the variation come from though, could be from the origins in ancient past, or just variate when Chinese went oversea and slowly change in last few decades....
At the end, by knowing how Chinese call each other, you will actually know what position the Chinese have in a family.
If you have more than one... like 6 brothers, 3 elder, 3 younger. Big elder brother, second elder brother and small (or third)elder brother. Big younger brother, Second younger brother and small (or third) younger brother~
Something about it just doesn't seem natural. The biggest thing that stands out is that you would use the past tense to say I just got up. So it would be:
Yeah, it's really hard to learn and use a grammar structure that doesn't exist in your native language. >__< I have a lot of trouble with using things like transitive and intransitive verbs correctly because English doesn't really distinguish between them.