It doesn't state it but would Arcane Eye be considered a creature?

no

By standard rules it would need to use the hide action to not be detected...

I guess it could be determined to not be detectable by sound, prints  or vibration. 

Quote from Kasiel >>

It doesn't state it but would Arcane Eye be considered a creature?

 I would probably consider Arcane Eye to be something that can be tangible, but is indestructible by material means.

I don't think it needs to use the Hide action as it is invisible.

An arcane eye cannot be detected, and is unlikely to be touched (although i would guess it is 1 inch in diameter from the description, even so, you can just make it fly). The way you remove an arcane eye would first require the ability to see invisible objects, then you could either attempt to trap it (difficult) or dispel it (easier).

It is invisible...

It could also be looked at as a form of ESP.  

Yuh

I believe it could be detected by any creature with Truesight, or any other entity granted Truesight via the True Seeing spell. I guess Detect Magic should also reveal the location of the eye, as a user of Detect Magic can use an action to reveal a faint glow around any magical object.

Although it’s not clear if Arcane Eye is in fact an object, the fact that it cannot pass through a solid barrier leads me to believe it is an object. 

Using Detect Magic would not reveal the eye as that spells description states you see an Aura around any VISIBLE creature or object.  See Invisibility would work however. Or living in an anti magic field....

 Is the normal vision also out to 30 feet or is that just the darkvision?

.....

Since it requires concentration, no, you can't.

Quote from Traveller_777 >>

can you have multiple of this spell up?

Since it requires concentration, no, you can't. 

By my calculations, you can move the eye approximately 18 kilometers, assuming you held concentration for an hour and had it move in a completely straight line. Somebody wanna check my math?

Maths Checked - incorrect answer

My working of how far it can move:

Duration 1 hour = 60 minutes = 600 rounds (6 secs each) 

600 rounds at 30 feet / round = 18000 feet / 3. 4 miles , or for those that work in funny numbers - 5486 meters / 5.5 km

Quote from Suriage >>

Maths Checked - incorrect answer

My working of how far it can move:

Duration 1 hour = 60 minutes = 600 rounds (6 secs each) 

600 rounds at 30 feet / round = 18000 feet / 3. 4 miles , or for those that work in funny numbers - 5486 meters / 5.5 km

 I'm doing my own research on this spell, and this math is accurate.  

For comparison, clairvoyance's sensor has a range of 1 mile and can't move.  So arcane eye is better as a spy tool to infiltrate an area and scout its defenses because it is mobile and has a longer functional range if time permits.  

Since clairvoyance takes 10 minutes to cast and has a range of 1 mile, I did some more math to compare which spell would arrive at a given distance faster.  Arcane Eye's sensor moves 30 ft per 6 sec, or 300 feet per minute, or 3000 feet (0.56 miles or 0.91 km) per ten minutes.  So if you need to see what's going on somewhere within a half-mile of you, it's faster to cast Arcane Eye and move the sensor there than use clairvoyance.  If the space you need to look at is a little more than half a mile to a mile away, clairvoyance's sensor will arrive faster.  Beyond a mile out to 3.4 miles, arcane eye will arrive faster because clairvoyance can't see beyond a mile in the first place.   

A downside to both spells is that you cannot instantly monitor a distant space.  This holds true even for higher-level divination spells like scrying, including magic items like crystal balls.  

I kinda of like the interaction between this spell and the 'Observant' feat {both in what it does and flavour). The downside side of this spell is it only provides visual information, meaning while you could use this to scry upon a meeting, knowing whom attended, you could not use it to know what was said. 'Observant' allows you to know what was said through reading there lips.

It can't move into another dimension but can the caster. Like cast it, then crawl into your rope trick?