me no sifu, but 10k is quite a big budget eh for someone new.

i'd suggest getting some mid-range slrs with not bad good controls like d7100 or 70d with a kit lens, or if you wanna save a bit, 2nd hand d7000 or 60d not bad too, then further increase your lens collection when you feel that the kit lens is limiting you

better than throwing going all in, and find out latr that photography is not for you, then would be a waste

happy shopping 

+1! You can save more with a new D7000 too (if you can still find one) since its much cheaper and performs almost similar to D7100~ Then start off with a normal 18-105mm F3.5-5.6 kitlens~ As pro3363 mentioned, you will be able to shoot from different range of distances with that lens; and from there you will discover which genre of photography you are more interested in, then only you invest in better lenses 

1: the sensor performance between fx and dx is almost day and night in high iso and also dynamic range. but if you don't use high ISO that often, it's more than enough to get a d7100 or 70d.

2: you might think that you don't need it, but that's because you never encounter with such situations before. it's really useful if you shoot group photo/ video or "close distance objects in details"(as you said), you will find the usefulness of it because you can check focus/ preview pictures in a totally different angle compared to fix screen.

3: most fx lenses are more expensive than dx lenses, but there are some exceptions. i can't really tell you each lenses since I am not using Nikon, but if you are interested in canon FF too, there are some top quality L lenses that are only 2-3k for new (17-40L, 24-105L, 70-200L f4, 100L, 200L, 135L and etc).

4: body made of aluminium or not, theses cameras can easily lasts you at least a few years. they are weather sealed too, means you can shoot in rain or outdoor (but they are not waterproof by any means). there's a reason why not all cameras are made of full metal, it's because manufacture can cut cost and also reduce the weight of a camera.

5: for battery, dslr batteries are charged off camera most of the time (not sure if USB can charge also?). that means you will get a external charger to charge your battery.

Lens are almost the same price if u compare the lenses with almost the same specs... For eg, 17-55 (DX) is also abt the same price as 24-70 (FX)... After all, u will be going to FX also one day

Colour is personal preference... Nikon has better dynamic range but some people jump to Canon because of their more natural colour... no need for me to mention, u know who u r  

Battery is rechargeable, but through external chargers...

Definitely go for Canon if u shoot a lot of videos

I suppose its just a comparison between D7100 and 70D The D600 might be abit overkilled for a beginner, especially so when you are still not sure you are interested in photography or not. Like what the other sifus have mentioned, some just shoot for the 1st few months, after that they just leave their DSLRs in the drawer. You lose less by getting a cheaper DSLR; and I think the D7100 will be much easier to sell than the D600 2nd hand
Furthermore there's the oil splattering issue that you might encounter- not worth it

Flip-screens can be super useful if you like to shoot couple selfies
And with those kind of screens there's more versatility i.e. noneed to lie down on the ground to take a shot at ground level haha

Even though you have a good budget, I would still recommend getting the kitlens (18-105/140mm for Nikon; 18-135mm for Canon) regardless of which camera you buy. The wide range of focal length will expose you to different types of photography that you may potentially like. After around 6 months of 1 year with the kitlens (assuming you shoot alot), then only you decide which specific lens you should buy