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.

You pick 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.
You pick 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.

Ten players the first way: every player is a separate spin at 50-50.
Exactly 5 against 5 happens in 24.6% of cases, and 7 against 3 in 23.4%. An even count is not a rule, only the most common of many possible outcomes.
If the count has to be even, the second way guarantees it: the names are drawn with removal and go to A, B, A, B in turn.

The same tool, a different job:

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 after each spin if you would rather what came up did not repeat.
Set Stop auto-spinning after and a number to limit the run.
With Save the list is written to the selected one — the line above the buttons says which. If none is selected yet, a list named after the page is created — Save never asks for a name.
With Save as new a second list is made without losing the loaded one. If the name is already taken, you are asked whether to replace the older one.
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.