She is somewhere between 13 and 19
Given the fact that she is described as a teenager, that puts her somewhere between 13 and 19 years old (according to the generally agreed-upon definition of a teenager). Understandably that's confusing when she is referred to as a veteran, but keep in mind:
Stat block titles are a convenience, and not necessarily a job description
The fact that she's given the stats of a "veteran" doesn't necessarily mean she has earned the title, it's just a convenient shorthand to point to a block of stats. For example in Waterdeep: Dragon Heist (the only adventure book I have handy), Urstul Floxin is described as a "glorified thug" in his flavor text, but instead of a Thug stat block his stat block points to a different archetype:
Urstul Floxin is an Illuskan human assassin, with these changes...
Stat blocks often match the character archetype, but some variations are possible, so take any Stat Block titles with a grain of salt.
You can choose what makes sense in your adventure
Given the age range of 13-19 you could make her 19 and still describe her as a "teenager", with 6 years of dedicated training under her belt to account for a CR3. You could just as easily have her in her mid-teens and attribute her high CR to her deep resolve, faith and determination, like for example Joan of Arc. If it suits your story, she could be 13 and have been trained from the age she could lift a sword, arriving in Elturel already capable of taking on a party of 3rd level adventurers- much like the character Hit Girl from Kickass.
Distances are determined by the DM--and don't have to be consistent
In the Introduction, it says this
Geography warps at the whims of the Nine Hells. One of the liberating aspects of this planar feature is that you don’t need to be fastidious about keeping track of where locations are in relation to one another.
You can decide how long it takes for characters to get from one place to the next. For example, the characters might need to travel 6 miles to get from Fort Knucklebone to Haruman’s Hill, and 60 miles to get from Haruman’s Hill back to Fort Knucklebone.
The section on using the map says...
distances in Avernus are impossible to gauge and locations sometimes shift supernaturally.
No scale is marked on the map, and the placement of locations is based on the memories of an intrepid yet insane cartographer. Distances and travel times between locations cannot be determined by studying the map and can change with each journey, at your discretion. Your players should never feel like they understand Avernus geographically, providing an unsettled and disorienting feeling as they roam the hellscape.
In short, the only one who can determine how far it is from Point A to B in Avernus is the DM. Things are not always in the same place you left them. Even if you are trying to return to the same location you've been to before, there's a chance you'll end up in entirely the wrong place
Using the map to chart a course from one location to another is unreliable at best. It helps if the characters have visited a destination before, but even that is no guarantee they’ll end up where they intended.
Maybe today it takes two hours to get from the Bone Brambles to the Arches of Ulloch, and you get there by traveling "North West." But the next time you make the trip, it takes three days and you have to travel in an entirely different direction to get there.
So, to put it simply...
The map is a crude guideline made by an increasingly crazy person. It is not reliable, and it gives no indication of the distance between points. Whenever players choose to travel within Avernus, it is up to the DM to decide how far they have to go and how long they have to travel.
Descent into Avernus offers no guidelines beyond this.
Where you say...
I know the rules say that a normal travel is considered a forced march and the Con saving throw that must be made is 10 + hour spent traveling to overcome a fatigue
Note that this is an optional rule provided for DMs to add to the game if they want to.
It is entirely up to the DM to determine distances between two locations, because "location" is more of a suggestion in Avernus than an actual rule. And the distances do not always have to be the same twice in a row...in fact, it is recommended that they not always be the same.
There are a few ways, as long as you carried around something to immerse yourself in
Firstly, you would need to carry around a box/bathtub/container/coffin large enough for you to immerse yourself in. When taking a short of long rest you can then fill it up with some of the below options:
Using the Decanter of Endless Water you could fill it with water most likely using the Stream or Fountain options:
How you acquire the Decanter is another question though, so you would need to ask your DM if you could reasonably have found/purchased one ahead of time. Since that the campaign apparently starts characters off at level 1, it may be a hard sell.
As Miniman mentioned you could also use Create or Destroy Water which is a 1st level spell available to Clerics and Druids. You can use it to: