The following is the best guide I've found to get to the point where you can reliably farm the higher difficulties. I've moved most of it over to protect against link rot.
Source: Loot Progress path for dummies
Getting the Gear
Suggested heroes: Adept/Apprentice (tower focus), Initiate/monk (tower focus), huntress/ranger (tower focus)
Starting build for each char:
Class: Hero stats - skills - Tower stats - resists
Adept: 0/0/0/0 - 0/0 - 65/120/26/120 - 0/0/0/0
Initiate: 0/0/0/0 - 0/0 - 91/120/120/0 - 0/0/0/0
Huntress: 0/0/0/0 - 0/0 - 120/120/91/0 - 0/0/0/0
Start the map with initiate/monk and play during combat phase with adept/apprentice. Focus on gearing up adept the most, but don't leave initiate left behind too much. OPEN ALL CHEST EVERY TIME.
Do each map as many times as you need to get enough gear to do the next suggested map. Also note, failing for the first time on a map doesn't mean you don't have enough gear, maybe you need to refine your tactic, build order. The original thread contains a diary post showing his gear progression (Here).
Here are some alternate tactics from the same guide.
Map #1: Medium Hall of Court (Pure Strategy or Survival)
GENIE IS REQUIRED. NOT OPTIONAL.
Build from starting mana.
Build before second wave.
Note: Start on wave 8, you finish faster, and if you choose medium PS, then it should be very easy, even naked. If you don't have any gear, just pick up whatever you find during the map. Don't forget to upgrade auras when they are at low health. Some info about Genie. When you are upgrading genie, upgrade the attack!
Map #2: Insane Glitterhelm Caverns (campaign)
Build from starting mana.
Build before second wave.
Optional build with huntress.
The following video is using somewhat modified tactic, because run speed and casting speed is low to play with two chars first wave. The characters are NAKED in this video. (2x speed, so you don't fall asleep)
Note: You can level the genie up very fast here without spending millions of mana on it.
Map #3: Nightmare Endless Spires (campaign)
Note: Chests can contain 90+ upgrade weapons and 60+ upgrade armors even after the first wave. The gear can exceed even ramparts.
Note#2: You can keep farming this in HC NM MM survival mode, and progress towards Map #6 and skip #4,#5.
Map #4: Nightmare Ramparts (campaign)
Start build.
Final build.
Note: The loot of this map doesn't exceed Endless Spires, but wanted to leave it here as a possible alternative.
Map #5: Nightmare Über Lifesteram Hollow MonsterFest
cubicleninja is missing the map, so can't provide layout. Check out the vid!
Note: Can be skipped
Map #6: Nightmare Mistmyre Forest
Idea for this as next step, and tactic by: Mirradin
Video by me:
Part 1
Part 2
As you may have guessed, the best way to get mana is to sell the numerous items that drop during each wave. Remember to pick up items to sell since there is a cap on how many items can exist on a map at a time. This mainly becomes an issue when the waves consist of over 500 monsters.
Once you can farm Nightmare Mistmyre you should be set to get 60+ million mana every 30 minutes. Here is a more detailed guide for farming mana there:
How to farm mythic gear & mana (60+mil 30 mins)
Best Answer
No, your Genie unfortunately does not put extra mana into the bank. When you're capped out, your mana does indeed go to waste.
You can use high level Genies on a character with high DPS to max out towers within 2-3 waves. Try to upgrade as often as possible or use your extra mana to power sustained abilities like Monk aura toggles, Squire buffs, etc., though the mana costs of these skills do rise the longer you keep them on, so this is not permanently sustainable.
You can verify this by looking in the bottom right corner of your screen. Whenever you earn mana that goes towards your banked mana (like at the end of waves for items on the ground, at the end of maps, etc.), you'll see your mana amount change. This doesn't occur during Genie use.