What’s This Blue Dome Projected Over My Back

That is the Charge Bar. The Charge Bar encourages you to use normal attacks, as it the fastest way for you to charge them and improve the effectiveness of the your Active Skills, where you have to manage your limited mana pool.

The amount of damage that you need to inflict to fill your charge bar scales with your level. If a low DPS weapon for your level will charge slower than a high DPS weapon for your level.

There are Active Skills such as the Embermage's Blazing Pillar (not entirely accurate skill, but good for building charge in grouped up mobs) that builds your charge at a faster rate, and there are skills that don't accumulate any charge (e.g. Magma Mace, Firebombs, Firestorm, and Hailstorm).

Each Charge Bar for each class works in a different manner:

With Berserker, when it's full, you will enter the frenzied state. You will run faster, attack faster, and always crit until the frenzy ends. It's worth noting that the frenzied state countdown doesn't begin until you hit something (after it's been filled up). You could potentially beat up that practice dummy in town to get your frenzied boost and then port into your destination and start the fight with a boost. The charge starts decaying a few seconds after combat and drains at a slower rate than the Outlander's charge bar.

The Outlander's charge bar works a bit differently compared to the other classes. As you fill it up, you will get the passive bonuses (Up to +10% Cast Spd, + 10% Dodge, +10% Crit, +10% Atk Spd) you get. There doesn't seem to be a break point threshold for each +X% bonus gain. The more damage you do, the charge increases, but it's also constantly decaying, so it's pobably the slowest to fill out of all the classes. Filling up the gauge up has no particular effect unlike the other classes. Additionally, it's worth noting that an Outlander with no charge will deal additional damage and stun the next enemy unit they hit. This bonus stacks with bonuses from shotgunnes.

The Engineer's charge bar has specific charge points (up to 5) and that a large number of their abilities use up in order to activate, and/or are more powerful (longer range/more damage) based on how many charges you have. The bar fills and drains much like the Outlanders, but a charge point seems to stay full longer after the charge point has been completely filled.

Embermages are very straight forward, when the gauge fills up, the Embermage goes into a concentration state (for 12 seconds) where all skills cost no Mana and they do 25% more damage on top of any bonuses (tiered, passives, etc.) they've invested in. It's best to save your more powerful mana heavy skills for this state.

I believe this shrine (or whatever you want to call it) has a chance at giving you an enchanted item. I've only seen one of these, however, so I cannot reliably say that you get something every time.

For me, this shrine appeared while playing as an Engineer. As soon as I paid the tribute, a voice said "You are fortunate" and a rare helmet appeared in the golden cauldron. The helmet was about the same level as my character's current one, but was a welcome piece of loot nonetheless.

There's a nice glowing animation that's played when the item appears in the cauldron; it was especially neat at night-time when my character happened to trigger it.