You can keep unspent red mana indefinitely while Electro is under your control. That means if you add a red mana during one step or phase, you can spend it during a later step or phase, or even a later turn. You will still lose other types of unspent mana as each step and phase ends.

If a red mana you add has certain restrictions or riders associated with it (for example, if it was produced by the last ability of Arena of Glory), they'll apply to that mana no matter when you spend it.

Once Electro leaves the battlefield, you have until the end of the current step or phase to spend whatever red mana you have before you lose that mana as normal. There is no penalty associated with this other than the loss of the mana.

Electro's last ability triggers without requiring a target. You choose the value of X as that ability resolves. If you pay the mana, a second "reflexive" ability triggers. You choose the target for that ability at that time. Players can respond to the reflexive triggered ability as normal, knowing the amount of damage that will be dealt as that ability resolves.