>>3381508>Looking to replicate this style of photography>$500 budgetOkay, so, $500 budget is pretty tight. But it's doable. Fortunately, digital cameras have been up to the task of photos like this for a while now, but you'll need to get something old and cheap to do it because you're going to need to spend some extra on glass and accessories.
So, looking at the three pictures:
1. Guy on the cliff. Clearly taken with a telephoto lens; probably ~300mm equivalent.
2. Girl jumping in the water. Most likely taken with a wide or a normal from a distance.
2. Guy on a cliff at night. Probably a normal or wide again, but the key with this one is that it's something that has to be good in low light.
So your idea to pick up a 35mm is good (normal, good in low light), but you're also going to need to grab a telephoto zoom.
Going with the d3300, you can get a copy on
keh.com for around $250 (remember to also get a camera strap if you buy from there). Yongnuo 35mm/2.0 for another $100. That leaves you with $150 in your budget for a telephoto lens. I'm seeing a Tamron 18-200 for $119 (which is going to be a fairly shitty lens, but has the advantage that it also gives you wideangle and can be your general walking-around don't-want-to-dig-in-my-bag do-anything lens), or a Nikon 55-200 for around $70 (which is also kind of shitty, but cheap, and probably a little higher quality than the third-party superzoom), or a Nikon 70-300 for around $100 (probably your best bet quality-wise, although I would echo everyone else's sentiment that you really should be paying more attention to weight).
Don't forget to also get at least a basic tripod, especially if you want to do shots of stars, plus a memory card. If those don't fit in your budget, maybe look at a used D3200 instead of the 3300--you don't lose a heck of a lot (although you DO lose AF-P lens compatibility, which means that 70-300 I mentioned won't work. Nikon is a compatibility minefield when it comes to lenses).