How do the teams come out even?

With the second way. The count always works out even and the order stays random.

Can the captains be set in advance?

Yes. They come out of the list and the spinning is left for the rest.

Yes, as many segments as there are teams.

The wheel picks the team — the segments are the teams and the players go through one by one. Removal stays off. The teams can come out 7 against 3, as with a coin.
The wheel picks the order — the players’ names go on the wheel, removal goes on, and those that come up go to A, B, A, B in turn. The count is always even.
Three teams and more — the first way adds segments, the second alternates in threes.
Balanced sides — the players split into two pots by ability and each pot spins separately.

Enter the options in the field, separated by commas or one per line.
Press ONCE for a single spin, or AUTO for a run of them.
Tick remove the pick if you would rather what came up did not repeat.
Set stop after N spins to limit the automatic run.
With Save you store the list under a name — a new one gets created, a loaded one gets updated in place. Names are unique, so a second list with the same name never appears.
With Share you get a link that opens the same wheel on another device.

Every segment has an equal chance and the list stays in the browser — nothing is sent to a server.