I'd trim it so it is neat and reasonably short. Neat but to long can still be a turn off.
As for the dress, the tie can be tricky if you aren't wearing a suit or at least a sport coat/blazer. Some people will think nothing negative of a tie with no jacket while others look down on it as a half assed job of dressing up. If you get an interviewer that looks down on the tie and no jacket you would have been better off just not wearing a tie. Even those who look down on a tie and no jacket seem to look better on an outfit that is well put together minus a tie.
If you own a suit, wear one. If you don't then dress a level or two above what the job requires. Wear slacks with the preferred color being black or charcoal, a fitted shirt in a conservative color (white or light blue), and nice shoes shined as applicable to the style of shoe. And make sure that the cloths are of proper fit. Tight and baggy go in and out of style for a simple reason, neither looks quite right. Proper fitting cloths always are in style for the simple reason they always look good. Wearing a well put together outfit that has attention paid to the details looks better then an OK outfit that happens to have a tie included.
Edit to add- If you do go with the tie (and I'm not saying tie with no jacket is a hard and fast rule, it can just be a gamble) don't go it alone. Use either a tie tack, chain, or bar that is conservative in design. Few things look worse then a tie flopping around all over the place. For extra attention to detail points any and all metal worn should match or at least be of the same tone (wedding bands or class rings don't have to follow this rule). So if one piece of metal is silver, all should match. If one is gold, all should match. Don't wear two or three different metal tones as it looks thrown together. And for the love of everything, belt and shoes should match. They can be a few shades off, but they should be basically the same. Belt width should also match the size of the loops on your pants, thin belt with big loops looks horrible as does a wide belt stuffed in tiny loops. Socks, a few shades off is OK so long as it's not drastic, should match the slacks not the shoes.