Pros:

- Strong Lane presence with constant poke
- High mobility for safe and fast roaming and warding
- Scales out of the lane like a beast
- Ultimate can be useful for helping team secure kills from the other side of the map (hence reasonably global pressure)

Cons:

- Not tanky and no defense orientated utility (e.g. Janna ultimate, Thresh lanturn), hence maybe suboptimal if your team lacks any defensive capabilities whatsoever.

Ezreal has no mana problems if all you do is spam q. Hence do so maybe auto attack whenever you get the chance.

His w and e are the major chunkers his mana pool low, if you use them too often you'll end up oom, hence just poke all day with his q, and only use his w and e for surprise poke (say if the enemy adc is already low), full engages or escaping.

His poke will also do surprising amounts of dmg on a low cooldown easily with a long range, hence if you land just a couple you can start to zone the enemy bot lane; also a subtle trick is to use q on healthy minions to reduce the cooldowns of your other skills, and hence have access to your other skills quicker.

In general your all ins or counterattacks to enemy all ins will be strong also, as you'll be auto attacking a lot with your adc; just remember elementary things like have to prioritize killing enemy adc as they'll likely be the damage threat and be wary of fighting the enemy adc if they managed to get a b.f sword and your adc only has a pickaxe etc, and le lv 2 power spikes.

!!! Remember to use EXHAUST well at the right times and you'll likely win.

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Poke
Poke
Poke
Bait engage on you from the enemy bot lane, e away
auto attack
Use exhaust on the enemy adc

Double Kill

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Remember to roam mid to unload a decent mount of dmg on the enemy laner if you get the chance 2, perfect to do when your adc backs and your wave is pushing.

When appropriate use your ultimates on other lanes, for example if the enemy laner is kinda low but not low enough for a all engage from your teams laner, but ur ulti will reduce the enemy laner to danger hp levels (usually only works against squishier champs like Riven or Teemo).

Also be sure to buy a sighstone early to stay safe. Brand support's highest win rate buy is a sighstone first.

Damage heavy AP mages like Brand and Ezreal can essentially scale out of the lane, primarly they'll be dominant during mid-late game teamfights and skirmishes (an ahead Brand support just has to use his R on the adc and team fights already half won, 0 counterplay).

Their most dangerous moment is during the laning phase as if their damage isn't a threat they'll become useless compared to more utility orientated supports such as Janna; a behind Janna can still use all her useful skills, a behind camped Ezreal or Brand will struggle to be impactful. Essentially they need to exit the laning phase without having majorly lost lane.

However, being damage heavy, you will still have strong lane threat. Hence you can win lane very easily 2 vs 2.

Hence, the major danger is to essentially have the enemy jungler or mid lane or even top lane camp and ruin all your fun when you are engaging too deep.

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Also be sure to use your w on your adc if you find yourself pushing down the enemies bot lane turret. It'll go down suprisingly quickly, with your ad auto attacks, your adc's auto attacks, and the decent lengthy auto attack speed buff from your w.

Be sure to keep warding heavily.

Primarily, even if you end up winning lane heavily and decide to roam to other lanes (very easy to do because of your mobility) or help your jungler make moves, you still have to ensure your adc is safe enough to farm.

It is very easy for you to roam, and have your adc suddenly go x/2 as the opposing bot lane makes a suprise play or maybe the likes of a Rengar uses their low counterplay ultimates to assasinate your adc whilst they're farming a bit too deep.

Essentially, your adc needs farm, and your team needs a farmed up adc for later game team fights and turret pushing, and your adc needs safety to farm (vision control can provide that safety even if you aren't nearby).

Given Ezreals high mobility it's very easy to find yourself on the other side of the map very easy leaving your adc vulnerable.

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Be sure to ward around objectives when it looks like they'll be fought over, e.g. Dragon. Or the side bushes in mid when there's many grouped around that region.

Because you are very mobile it's safe to roam.

Don't hold onto your ultimate also, as it's on pretty low cooldowns (especially if you are able to spam your q).

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By now you will have a decent amount of AP also likely, and maybe even have the likes of a Rylais.

Ulti'ing into the enemy team can slow them all, which looks pretty funny.

Just keep poking and poking, support your team by roaming and using your ultimate if there's a fight far away.

Be sure to keep Baron warded.

You'll be a major damage threat by now.

You will likely win team fights and skirmishes just because of the surprising amount of damage you can do even though your build doesn't maximise damage.

Be sure to stay with your team, exhaust the right targets and you'll win.