Crossword

For example:
Across
1. Opposite of complicating (11)
3. Last noble gas alphabetically (5)
4. Position to interview for (3)
6. 365 day periods (5)
7. $1000, informally (5)

Down
1. 30+30 (5)
2. Short relationship (5)
5. Opposite of good (3)

Across
1. One of the Down answers in the example (but a different one from 2 Across and 10 Across)
2. One of the Down answers in the example (but a different one from 1 Across and 10 Across)
4. Shortened forms of words
8. One of the Across answers in the example
10. One of the Down answers in the example (but a different one from 1 Across and 2 Across)
11. Smallest prime number
13. Arch of colors formed in the sky
14. Sick
15. The national bird of the USA is a bald one of these

Down
1. Factor of 1 Across (but a different one from 7 Down and 12 Down)
2. Opposite of above
3. Most populous city in UAE
4. Synonym of 2 across
5. Supernatural drama television series, ____ the Vampire Slayer
6. Block of steel, silver, gold, or some other metal, typically oblong in shape
7. Factor of 1 Across (but a different one from 1 Down and 12 Down)
9. Sharpened point of a quill pen
12. Factor of 1 Across (but a different one from 1 Down and 7 Down)

Hints

I have solved the clues, but I am struggling to organize a crossword. Can you help?

You will need to construct a crossword grid with your answers, but it won't be a typical square grid with rotational symmetry.
With the top section, you know that both 1A and 1D start at the same cell. 2D's first cell appears between 1A and 3A, meaning it's likely that 2D starts somewhere in 1A.
Writing out all your across clues into a general grid shape and using trial-and-error with down clues may be the quickest way to the solution.

I have solved the example, but the one below is so much harder! How can I break in?

You should be able to note some properties of what you are forming based on the example (for instance, the size of each letter, amount of space between letters) and that should help constraint your actual crossword.