Using the link mxyzplk provided as a comment to your question:
TYPE OF JUMP -- DISTANCE (IN FEET)
Running Long-Jump -- Athletics check result
Standing Long-Jump -- Athletics check result, divided by 2
Running Vertical Jump -- Athletics check result, divided by 5
Standing Vertical Jump -- Athletics check result, divided by 10
Any jump check can be made as part of a move action. Your distance moved cannot exceed your movement allowance for a round. If your jump if longer than that, I (as a GM) would rule that you travel the rest of the distance the next round and cannot take your standard action that round (unless you did it before your move action). I'd encourage a player to use their standard action as a second move to complete that jump. It's worth mentioning that Running is a DC15 Atheletics check that automatically improves your speed by 1 rank (on the Rank and Measure chart) for a round. For an average human being without powers, that takes them to movement rank 1 (from 0) - 60ft/round. With a 15-foot running start, that's 45 feet of long jump distance before you have to take a second round to land.
To answer your specific questions: the online resources aren't clear as to how much distance you must run to make a running long jump. I seem to recall that 3.5 required 10-15 feet, but I don't have my books on hand. As a GM, I'd say 15 feet is a reasonable distance - a healthy individual can get up to full running speed within 15 feet.
Jumping is part of movement. Running boosts your movement speed by 1 rank. Therefore, your movement doesn't end when the jump does, unless it reaches or exceeds your movement speed. So you're welcome to make a running jump, land, and keep running up to your maximum movement distance. Thus, in your example, the person trying to make a running jump across a 15 foot gap would have to beat a DC15 Athletics check to run, run 15 feet, roll an Athletics check and beat a DC 15 (minimum), and they would still have 30 feet of movement this round, plus a standard action.
Now let's take a look at what this means, especially taken to ludicrous extremes:
What about someone with absolutely ridiculous jumping ability? What about someone with a +500 Acrobatics skill? Someone who can routinely running jump further than their movement rate?
In my book, it stops being a skill check at that point and should instead be the Leaping power effect.
But I didn't write the rules. Someone, somewhere, is going to want to make someone who is so incredibly athletic that they can defy the laws of physics without superpowers.
So lets look at someone with high Athletics, named Runman.
At +15 Athletics, Runman can't fail a running jump. He will never fail to run when he tries, so his movement during a run will always be at +1 rank. His average roll will be a 10, for a DC25 running jump. He will travel 31-51 feet during a 15-foot run and a running jump.
At +20 Athletics, Runman will travel 36-56 feet during a round. This is similar in effect to the Leaping 1 Power Effect. This is the absolute best a character can do at Power Level 10.
At +30, Runman will travel 46-66 feet during a round. At this point, his best jumps (a roll of 15 or higher) will begin exceeding his ground speed, but just barely. This is still equivalent to Leaping 1. At this point, there is nothing Runman can't do that is athletics based. He could win gold in every Olympic medal that uses Athletics as a skill on the absolute worst day of his life, and would immediately be hired by any pro basketball, football, soccer, etc team. That team would likely not lose many games over the next decade. A computer hacker with this level of skill could hack SHIELD as a routine check. This level of skill would only be possible with a Power Level 20 character.
At +105, Runman can move 121-141 feet in a single jump. This will take him at minimum 2 rounds, and is a really expensive way to almost go as far as Leaping 2 can take you in a move action. There is no Athletics task Runman could conceivably fail at, and Plastic Man would envy his flexibility. He could replace an entire baseball team, outdunk Michael Jordan in his prime, and finish a swim meet just ahead of Michael Phelps. He can jump further than someone with Leaping 2, but just barely. Someone with Leaping 3 would outdistance him by a significant fraction of a football field. This character would be an astounding PL95, with more power points and higher caps than any non-PLX character.
I could keep going, but I think it's clear that while you can move fast and far with a running jump, it is primarily geared towards people who don't have much in the way of movement powers.
If your characters intend to jump a lot, encourage them to take Leaping 1. In any superhero game, it's easy enough to describe as 'innate ability' or 'training' and will greatly simplify the mechanics (and reduce the number of rolls). Toss in Move-By-Action (an Advantage costing 1 power point) and you can exceed the jumping capabilities of Runman (+30) handily, without spending 15 power points on a single skill.
Edit: I'd forgotten (as it wasn't relevant to the 2nd half of my answer) the PL limits upon skill checks.