Do you still have to be a Wizard etc. to use this? Because I was thinking about doing a campaign where anyone can summon an elemental under the right circumstance, and this (along with the magic items of the same category) would fit the bill perfectly. 

You should be able to use this regardless of class I would imagine. There doesn't seem to be a started limitation.

Do you still need a surface of water for the elemental to manifest like with the conjure elemental spell?

Not exactly. You need to have the bowl filled with water. You are sort of casting the spell by summoning the elemental from the bowl itself. So the bowl needs the hydration.

It also looks like there are no limitations on who can summon the elemental. No class, race, level, or even Attunement restrictions. Super good item.

Do you still need to concentrate or because it’s the bowl doing it do you not concentrate?

Doesn't look like it needs water to be physically put inside nor concentration.
I imagine the item refilling with water at the dawn. As in recharging it's ability.
It also doesn't say you need to concentrate

As far as I know you do need to concentrate since it says as if you had cast the conjure elemental spell, which seems to be the consensus looking around but if you have any source that says otherwise I would be happy to be wrong. Also the item is a bowl, it is not exactly a good closed container. To me it makes no sense running around as an adventurer carrying a bowl filled with water since it would spill all over considering that it says nowhere that water inside this bowl defies gravity and stays inside the bowl. I think you need to pour water into it or dip the bowl inside a water source, which is balanced considering that usually you need 1 minute to cast the spell while you only need an action to cast it once you have actually filled the bowl. Personally I carry with me 6 waterskins to fill the bowl which limits its utility if I get jumped in a combat encounter and there is no access to water but at least it is not immersion breaking like carrying water in open containers like a bucket, 3 jugs/pitchers, directly inside the bowl or in something ridiculous like 3 pots full of water. Of course it doesn't make much sense that there aren't closed containers that contain exactly 3 gallons and the only option for a closed container capable of housing 3 gallons of water is a 70 pounds heavy, while empty, barrel with a 40 gallons capacity in dnd, but that is a whole other discussion.

Typically magic items that replicate or cast spells will outright specify if it requires concentration or not
So it's up in the air. But as it doesn't say you concentrate. The likelihood of it requiring concentration is lesser than the likelihood it does not
And to keep on that subject. It does not say anything about needing you to put water in. It would say so if it did
And your comment about a "source". I don't need to provide one. This is my opinion, based off of my reading of the numerous other items in the game.
I don't really need to cite any source. As I don't need to. It's my opinion. And unlike some people, I'm not trying to force my opinion on others as "proof"

And it's a magic bowl with clearly magic water. And balance doesn't come into it.
What's your backup to this assertion if you look at it's earth counterpart? it's a rock. That's it.
If it was a thing for balance, all the other versions of the item would have one.

It sounds like either yourself or your DM have read too far into the item, and are attaching trappings to it that aren't there.
Which is fine. But that doesn't make the way your group uses it fact.
but like I said. If the item doesn't say it, it doesn't do it.
That's the way items & spells in 5e typically work

Funny, for such a powerful item, I don’t even think this even requires attunement.

Conjure Elemental is an interesting one.  You maintain concentration not too keep the spell in effect, but just to keep control of the elemental.  Also, in terms of fluff, you need a piece of the element of the elemental’s type, present to summon through, but it’s a bowl, so I doubt that’s a problem.

Your first comment about concentration is wrong. Per the DMG:

Some magic items allow the user to cast a spell from the item. The spell is cast at the lowest possible spell and caster level, doesn't expend any of the user's spell slots, and requires no components, unless the item's description says otherwise. The spell uses its normal casting time, range, and duration, and the user of the item must concentrate if the spell requires concentration. 

Your second comment about it not needing to be filled with water....

The first sentence of the item description starts "While this bowl is filled with water". That means it can be empty which makes sense because, well, its a bowl and bowls just kind of work that way, magic or not. It does not say anything at all about the bowl being magically filled all the time, or having the ability to somehow fill it self with a command word or at dawn. The description also specifies a volume of water that the bowl can hold, which would be irrelevant if the bowl did not need filled. 

As for your third comment about responding to someone asking if you had a 'source'. Many campaigns run RAW so a player questioning if your opinion, which you publicly posted for peer review, was derived from a 'source' seems perfectly reasonable. But this is just my opinion, based off... well, you know the rest.