Electronic – Fuse symbol on toroidal transformer

In short: no.

In "long": it doesn't mean that and, while it may be possible to be so, don't forget that the current capability is directly related to the cross-wire section (area), which means making it generate more than it was planned to will most surely heat it up and, possibly, permanently deteriorate the transformer.

However, seeing that you have 3x8V, it may be possible to connect the windings in parallel, thus granting you the ability to deliver 3 x current, but for that you need to separate the windings so that they are completely separate, then connect them properly in parallel (hot end to hot end), i.e. not in anti-parallel.

Even so, I would discourage this because the windings themselves may not be equal, that is, the 0-6 one may have the average turn length less than the 18-24 one would, meaning that the internal secondary impedances will differ, resulting in other possible cases of deterioration. If, by any chance, you get here, equality may be brought by inserting series resistances on each winding (two at least), at the cost of more losses.

Primary: 220V Secondary: 12+12V Rating: 5A

This notation generally means that there are two secondaries, each rated at 12V and 5A. It could also mean a center-tapped secondary that's rated at 24V @ 5A overall.

If I use it as a 24V transformer, is the total current 2.5A?

No, if you put the two secondaries in series, you get 24V @ 5A.

What happens (besides heating) if the transformer's current rating is exceeded?

Isn't heating bad enough? Transformers generally aren't all that good at getting rid of heat (high thermal resistance between the windings and ambient). Once the internal insulation breaks down (or catches fire), it will fail fairly catastrophically because of the shorted-turn effect.