There is a small gap between the spell steal and the spell cooldown reset (Resets the spell cooldown before it changes the spell to the stolen spell). Because of this, you can cast a spell 2 times back to back. This can be done by casting the spell, stealing another spell, and in that gap casting the spell again. (This combo is difficult to do, and needs a lot of practice to perform successfully.)
If a spell with a long cooldown is stolen then used, you can reset the cooldown by first stealing a different spell then re-stealing the original spell. If done in this manner, the spell will have a reset cooldown. Re-stealing the spell directly will not reset the cooldown, only refresh the duration of Spell Steal. Example: Steal Elder Dragon Form, use it, then steal another spell like Fissure. If Rubick then steals Elder Dragon Form again, it will be instantly usable without having to wait the 115 seconds since it was last used.
If the target enemy Hero has Aghanim's Scepter but Rubick does not, then he will not steal an upgraded version of the spell. However, if Rubick has an Aghanim's Scepter then he will steal an upgraded version of the spell even if the spell's owner does not have one.
Even though the UI might make it look possible to have two different stolen spells at a time, this is not possible except for when stealing spells like Illusory Orb that have a secondary ability built in.
A full list of unique interactions with spell steal can be found under Spell Steal Interaction.