I am not very familiar with Wolsung (I, in fact, just downloaded and read the basic manual in order to answer your question) but I have some experience with similar games and I think I may be able to help.
Pages 4-5 of the Test Drive document state:
"When a conflict begins, the GM and players discuss what they
want to gain in this conflict and what they are ready to risk. The
stake must be known before the conflict begins...
...In addition, every character that lost a conflict, temporarily loses
one level of the appropriate attribute (Brawn for combat, Agility
for chases and Composure for discussions). If you test an attribute
that dropped to 0 you cannot re-roll. The attribute regenerates at
the beginning of the next game session."
So, unless this system is removed/significantly changed in the proprietary rulebook, when you negotiate consequences for a chase scene I think it makes sense to handle these issues. To use your examples:
A foot-chase:
Escape from the super-goons as a party or the slowest party member gets captured
-or-
Scatter and test to escape from the super-goons individually and with a bonus, but get caught if you can't evade your pursuers.
-or-
Escape as a party from the super-goons, slowing down to help the slower members cover their backs, but risk getting caught as a party
All of these should obviously carry different positive or negative modifiers to the escape rolls for the various characters (I'd probably do neutral for the top, positive for the middle (but the party is separated), and negative but with a free re-roll to the lesser party members for the bottom). If, halfway through the case, the party decides to jump in the back of a passing truck and succeeds at getting in but fails to make their finisher roll, I'd have more super-goons show up in classy black Lincon Towncars and tail them, continuing the chase, but I would treat it as a new conflict (since the consequences have presumably changed) and renegotiate with the party.
As for how to deal with multiple characters, each rolls separately. If you had a BBG (3d10) and his nefarious apprentice (2d10) and their trained deadly ninja-monkeys (1d10 extras) fighting against the valiant Super Six (2d10 PCs) every character would roll their own dice except the monkeys, who act as a group. Each entity goes on its own initiative.
As for what to do when one of the players loses a challenge while the other players still have not: The players have lost. This is important and works both ways. When any member of a side has lost all their markers and takes another hit, that side loses and suffers the agreed upon consequences, which I would almost always make sure included phrases like 'the weakest party member', 'the tallest party member', 'the tastiest-looking party member' or 'the incompetent minion responsible for this unacceptable failure', 'the expendable monkeys, cause I'm more important', etc.
However, only those characters who actually lost the conflict take the 1 attribute point additional penalty.
As for what happens when there are more PCs than enemies: It depends on what the PCs try to do. If they run as a group (option 3 above) they can certainly all be caught but if they scatter (option 2) they certainly can't be. It all depends on what people decide to do and, more importantly, what consequences are negotiated as a result.
As for whether or not PCs (or enemies) need to outrun everyone in a group, the answer is actually no, technically. Like I mentioned above, once one part of a team is defeated in Wolsung the whole team has lost. The consequence for winning, however, probably isn't 'get away' but rather 'lose the slowest opponent'. If you find chases are taking too long, I suggest not refreshing challenge markers for the losing team between conflicts (but refresh markers on the winning team, as the sight of some of the pursuers falling behind/ the capture of one of the fugitives gives a boost in morale) and encouraging finishers.
The Car Chase Case
This would normally be a test made just by the driver of the vehicle against the driver(s) of the chasing vehicle(s), with a consequence agreement like "We escape or we are caught", however your specific situation may make this undesirable.
If the players decided to all roll chase tests (as opposed to having just the driver roll) I would first ask them to each describe how they are contributing to the chase in a meaningful way. If the agreed upon consequence for the group was "we are caught" then when one of them fell I would describe how X bad thing happened to them (got shot or whatever) and without their help the chase was lost. Again, a more reasonable consequence agreement for that (unusual) situation would be "We escape or the team member who did worst is incapacitated".
It seems to me (may just be my Shadowrun background here) that the most common kind of drawn out chase scene involves combat simultaneous to the escape attempt. In that case, which I expect would be reasonably common as far as car chases go, I would overlay a combat over the chase, with the drivers contesting drive (or whatever) and using Agility to determine Challenge while the rest of the group contests firearms with the armed goons in the other car and uses Brawn to determine challenge. The consequence agreements for each group (drivers, shooters) would be different.
In any case, the core of the issue is keeping track of 1) who is involved in the conflict governed by a given consequence agreement, 2) who/what should be effected if a conflict is failed, and 3) what the right level of detail for a given scene is. If you find some other possible interpretation of when conflicts end, you should add 4) the end condition of the conflict and its relationship to the conflict itself.
