2. First we have to look at upgrades. Your healing right now is about average for your level, however there are a few things you can look out for.

Your weapon is actually the first thing you should look at upgrading, although it may sound strange the Magic Damage from a weapon as well as the Mind increase is one of the biggest factors for how much we heal for. So I would focus on getting a higher level weapon. Next would be Chest/Legs, followed by Hands/Feet/Head, then Belt, and finally jewelry. Or whatever you can grab from dungeons as an upgrade.

Don't worry about Secondary Stats such as Determination, Crit, or Spell Speed for now. You want the most Mind you can find out of any piece of gear once you hit 50. You can worry about Secondary Stats if and when you decide to take on harder content (such as Coil, Extreme Primals, etc). There are plenty of helpful tips and guides on the subject in these forums for what you should go after as a healer (be it whm or sch).

Although having just checked your lodestone profile, your gear is actually fine for your level at the moment. I've healed in worse during my progress to 50. My upgrade tips still stand though as you hit 50.

3. You won't get kicked, but you must tell the group that you are a brand new 50 and big pulls should probably be avoided. There are people who like to do Speed Runs through dungeons and they will run through entire sections pulling every single enemy they see, and then AE it all down. As a brand new level 50 Scholar more then likely you won't be able to handle this until you get some better gear, so be aware of that.

4. Succor usually isn't needed for your group before a pull, even most bosses its not an issue because it will fall off well before any AE damage happens (typically, not always). Adlo on the Tank before a pull is fine. DPS wise this is up to you and how comfortable you feel with the tank. Although the earlier dungeons are far easier to just let your Fairy heal for the most part, some of the higher dungeons can hit a bit harder, and tanks aren't always well geared. You already cast Sacred Soil at the start, which isn't necessary but does help especially with under geared tanks.

Fairy placement is also one of those on-the-go type things. Not all fights are as forgiving to your fairy and it will be more or less trial and error to where you can or can't place your fairy. For the most part I've always kept mine following me in dungeons, unless a particular boss fight got it killed that way. However they are resilient little buggers and can take quite a bit of punishment.

As a side note, you also want to get your Cross-Class skills in order to help you out a little more. Here are the recommended Cross-Class skills for a scholar. In no particular order here we go:

Cleric Stance - Which you already have.

Protect - Although it doesn't come with the added magical defense, it does help.

Swiftcast - You will need to level your Thaumaturge up to level 26 in order to get this one, once used, this will make your next spell instant cast. This is mostly used to Raise people who have died in combat (such as during a boss). Can also be used for other things, but for the most part SCH will save it to get people back up.

Stoneskin - Conjurer level 34 spell. While not required, it does help give a little more mitigation before a pull, or on boss fights where you know there's AE damage, but Succor won't last long enough to help block the damage.

Surecast - Probably the least used Cross-Class spell in the bunch, this will allow your next spell to be cast without interruption. Basically if you have some enemies beating on you, or a particular boss move you know interrupts your casting, you can use this before you throw out your next spell. Again this one isn't used very often, but it can be useful in the right situation.

Those are the main 5 you want, you can also add in Aero for extra DoT damage. Cure obviously isn't needed because you have Physick, they are identical to each other. Raise also isn't needed since you have Resurrection instead.