The professional way to do any selection is to use a layer mask and get to work. With that kind of shape, using a path would give you a nice result too. A layer mask will hide everything you want and that's a good way to apply any pattern on anything, and even duplicate that mask or change that pattern without having to re-select the shape again.
The "other" way is to use the wand tool; it's not the pro way but it can give ok results for some projects.
The reason why you didn't succeed using the wand tool is probably because you need to adjust your "tolerance". The tolerance tells the wand tool how many more colored pixels should be selected around the area you selected. The higher the tolerance, the more pixels will be selected; that's a good thing when you need to select the anti-aliasing for example.
With your graphic it's very easy to only have the swoosh with the inside pattern left.
Select the wand tool and type "16" on the top menu where the word "tolerance" is.
Then simply click on each section of red + black while holding the SHIFT key; it will add all the new areas you selected to your selection. If you see too many parts don't get selected, simply raise the tolerance.
Then go in the menu "select" and choose "inverse"... and delete the selection. It will delete the outside part of your swoosh.
A suggestion: Make a layer mask with that selection now that you have the swoosh isolated!
By the way, maybe the reason why your image became grayscale when copying into a new document is because you didn't select RGB or CMYK color mode... but grayscale.
Unless you mean you see this anti-aliasing issue as shown below on the image on the left. In this case simple use the trick above to select your swoosh again and add a black shape on a layer UNDER the swoosh to hide the lines.
Note this "inverse selection" and "holding shift key" tricks down, you will certainly need to use this thousands of time in your life if you keep doing design projects!