If you become invisible, can you use the Hide Action without having a place to hide? Also, if you hit someone after you performed the Hide Action, would you be able to use a Surprise Attack? If it matters, this assuming a level 17 rogue with the assassin subclass.
Invisibility, Hiding and Unseen Attackers
When you are invisible, you gain all the benefits of being an Unseen Attacker, but are not hidden.
Combatants often try to escape their foes' notice by hiding, casting the invisibility spell, or lurking in darkness...
When a creature can't see you, you have advantage on attack rolls against it. If you are hidden--both unseen and unheard--when you make an attack, you give away your location when the attack hits or misses.
Because you are invisible, you should be able to take the hide action without needing cover, because there is no line of sight. There are only a few mechanical differences (at the end of the above quote). between being unseen and being hidden, so depending on what you want to do, you might not even need to hide.
I assume you mean Sneak Attack not surprise attack.
Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll.
Since being unseen grants you advantage, you can sneak attack without hiding, just by being invisible.
If you are talking about Assassinate:
In addition, any hit you score against a creature that is surprised is a critical hit.
Then, no. If you are engaged in active combat, it is unlikely a DM will say the target is surprised:
The DM determines who might be surprised... at the start of the encounter.
This is echoed by the advice/intent of Rules Designer Jeremy Crawford:
The surprise rule applies only during the first round of a combat in D&D.
On any round, you might not be able to perceive a foe, in which case you follow the rule on unseen attackers and targets (see p. 194 in the Player's Handbook).