I don't know who told you that descending intervals weren't as important as ascending ones but in my opinion they're wrong. Music doesn't always ascend in melody. It's better to pay equal attention to descending and ascending intervals. Music goes both ways.

Here's an exercise. Say your practicing the interval of a perfect fifth. You would play A and then up a perfect fifth to E. Listen and then sing (or hum)the interval as you play it. Then once you got that, do it in reverse. Play E and then down a perfect fifth to A. Repeat the steps above. The entire time you are focusing on a perfect fifth, one interval. Go through all the chromatic notes. So next would be Bb and F, and so on. Focus on the range, not the notes themselves and I quartantee if you do this everyday for a week. The sound of a perfect fifth will be sticking in your head. As you become confident, try singing the preceding interval before you play and then check yourself. Once you can sing the second note and get it right, you know it.

Make sure you sing your intervals, it's the only way to really get them to stick in your head. If you can sing it, there is no doubt that you know it.

Don't worry about being alittle flat or alittle sharp. You don't have to sing perfectly in tune, just as long as you get the range close and your not singing a different interval.

Also for extra support use the "do-ra-mi-fa-sol-la-ti-do" thing. This will help if your having some difficulty or feeling stuck.

Yes, anything that involves using your ear in music will help improve your ear. Improv, learning songs by ear, anything and everything where your using your ear in music helps. Picking out songs that you like and figuring them out yourself is one of the best and most rewarding processes of ear training. The excerises above are the groundbuilding steps. Pay attention to the musical quality of the stuff you play, it will reward you ten fold.