References
From Episode 1 p22, this is the allocation I assume you are referring to:
As an effect of the way in which the adventurers have impressed the dragon council, it now falls to them to allocate the dragons that have pledged their service to the factions.
From Episode 6 p59:
Five ancient dragons make up the council charged with deciding their metallic kin’s response to the cult. Though they are not necessarily the wisest or most powerful specimens of dragonkind, all are well respected. Any decision made by these dragon councilors will be accepted by the metallic dragons as a whole.
and
To secure the cooperation of the metallic dragons as a whole, the party must conclude this episode with at least three dragon councilors having a friendly attitude and with none unfriendly
and p61:
When the characters have reached a satisfactory agreement with the dragons,
Not directly related but useful as guidance, from Episode 9 p86
Chromatic Dragons. The exact number of chromatic dragons present at the Well of Dragons is up to you, and could range from a few dozen to a hundred or more.
and p87
Metallic Dragons. The metallic dragons will be outnumbered by their chromatic cousins. However, they cooperate with allies better than the evil dragons do, giving them a greater impact on the battlefield.
Discussion
Like a lot of things in this module, DM discretion is involved.
The criteria for getting the support of all metallic dragons is clear. It seems to be implied that you can get partial support as well. So having got support, full or partial, how many dragons is that?
The information in Episode 9 gives you guidance for the total number of metallic dragons available for the final battle. Even if you operate at the lower end of the range, the number of dragons available at that point is ... adequate.
Remember, the dragons are preparing for the final battle themselves and they have things to do, people to eat, sorry meet, etc. and the PCs have to negotiate an agreement with the metallic dragons. Surely the number of dragons provided for immediate deployment would be a key part of that agreement?
The Council Scorecard also needs to be considered. If the PCs get no dragons then they are at a disadvantage in the final battle but the suffer neither advantage nor disadvantage with any of the factions. If they make concessions to get the aid of the dragons (and they will probably have to) then they hurt their rep with most factions. Giving a faction support can repair this (partially in some cases) and not giving a dragon can hurt them further. The dragons are therefore a bit of a poisoned chalice; gaining their support may cost the PCs the support of one or more of the other factions.
So, do what any good DM does in those circumstances ... cheat. Give the PCs enough dragons so that their choices matter.
This adventure takes a lot of forethought.
As the DM it falls on you to decide how much you want to either adapt your world to the players and how much you want to allow the players to change the world.
For example, you may have already decided that Tiamat is not ever going to rise in your world. You may either "redo" or otherwise give the PCs another chance at an asset they have failed to acquire. For example (no spoilers here), the PCs could need to save a village from an attack by a band of lizardmen. As a reward (unknown to them), they will be given the Amulet of Gygax, a key asset to advancing the story. Due to poor luck, and poor decisions, the lizardmen win and the PCs retreat. Rather than simply saying, "Well, you think you should try again, right?" or something along those lines, you could say, "That village is destroyed; as you lick your wounds, the lizardmen appear to be sending scouting parties down to the next village."
If you've decided that the PCs can affect the world, you might decide that the final battle is inevitable, but the PCs' success isn't. At that point, the campaign becomes one of surviving in occupied territory (and maybe plotting an overthrow).
The three items you ask about really boil down to a question (I think) of "How can I make this story fun for the players without railroading them?"
The biggest piece of guidance I can think of on that is to talk to your players about where they think they are in the game: "So Bob and I are preparing for the return of Lolth so when Tiamat shows up we'll have an ally."
Remember that this is a collaborative effort.
Best Answer
I've played through Rise of Tiamat a few times with various DMs, and all of them had different approaches to it. The first questions you need to ask yourself is: "Do I want PC death in this campaign?" and "Is PC death a bad thing?" Let's keep it mind that going against a cult backed by dragons and potent casters is in itself fairly deadly, and no fight with a dragon should be taken lightly. Now if you may want to prevent player death for several reasons, but keep in mind that only sending the party against encounters that they definitely can win dulls the excitement somewhat.
Now, should your concerns remain, consider talking to your party before the start, or shortly after the beginning, of the campaign. Explain to them the severity of the situation, and that not all fights are meant to be won. Sometimes, the right strategy in a fight will be to flee, and even then that might not work. Encourage them to plan ahead, and if a character dies take a break after the game to discuss the consequences of this death on the party and their state of mind.
Now, to address the actual questions:
1) Assessing party strength and capability: Given the various different compositions a party can take, it can be hard to accurately pinpoint how difficult a certain fight will be for a group. The best way to give your group a preview of the fight is to pit them against a similar, but weaker, enemy first. Like a vaccine does to an immune system, this precursor to the actual challenge will allow the party to formulate a strategy and learn of their own strength and weaknesses against that type of creature in order to adapt appropriately. Likewise, research will let your group find out more info about their foes. Consider having them talk to a professional dragon hunter or a draconic loremaster for more information. If they encounter a town ravaged by the dragon they're currently hunting, or the wreckage of another ship, in your case, they might get a better sense of that monster's destructive potential.
2) Can 5 level 10 characters take down an adult white dragon: Now that heavily depends on group composition, and with the given info it's extremely hard to assess. Needless to say, with bounded accuracy technically a group of mid-level characters can technically take down almost any high-level monsters if they roll well and the monster rolls poorly. Also, if your group is a gang of multiclassed, optimized badasses, they might have no problem taking it down. That said, the encounter should be a hard or a deadly one with that kind of group. The short answer is: maybe. The long answer is maybe as well, but with a lot of needless explanation attached to it. But level 10 characters have access to spells to scry and bring back the dead, which will allow them to prepare, and lessen their losses as well.