The Crafting Chamber is a feature that Senseis gain access to after beating 3-2 in the main campaign. Its primary feature is acting as another supplement to assist Senseis in getting more materials for their students.
Utilizing Keystones, Material Synthesis gives Senseis 5 random sub-nodes that will give them different items. Senseis can only pick one to craft, however. In addition, the sub-nodes are randomized each time, and thus you cannot guarantee whether or not you'll be given a node that lets you craft a specific item such as a gift or furniture each time you utilize Material Synthesis.
You can unlock up to 3 sub-nodes in one crafting node, with sub-node 2 requiring double the amount of Keystones used in sub-node 1. However, in exchange, you can get much more specific materials, such as specific type of furniture, though it is still not guaranteed that these materials will actually pop up still.
To unlock sub-node 3, Keystones are not used but Elephs, with 5 Elephs being the cost to activate. You can get student elephs here, but you are not guaranteed a specific student. This is generally not worth it as Elephs are hard to come by and may be better off spent on your students especially if you are a newer player. In other words, it is better to stick to sub-node 2 at most for crafting purposes.
Crafting is not instant and will take some time to complete. You may utilize a crafting boost ticket to make the crafting time instant, however. The ticket cost is dependent on how many sub-nodes you have unlocked, with 1 being the minimum and 3 being the maximum. These tickets can be obtained at random from simply doing normal or event stages. You can also buy them using Total Assault currency, but it's not really worth it.
Keystones can be obtained through doing tasks such as daily or weeklymissions. They can also be obtained through gacha, where the amount of pulls you have (if not converted to a spark) will be converted to the same number of Keystone Pieces at the end of a specific banner period.
On the second tab, we have Material Fusion. Here, you will use materials that you already own to transform them into something else, usually a related type of material.
As an example, to create a Gift Choice Box, you will need to use various student gifts as materials.
You will also be required to spend Fusion Keystones when using Material Fusion, which can be purchased via the Shop while the currency itself can be obtained via doing Joint Firing Drills. The type of Fusion Keystone needed corresponds to the rarity of the item you'll be crafting.
The benefit to Material Fusion is that there are specific items you can craft that can guarantee you certain materials, like Tech Notes for a specific school. The ratio of the cost to craft items is 2:1, so if you want to craft 5 choice Gehenna Tech Notes, you will need to use 10 Tech Notes as materials. While this can be pretty expensive, it is also a good way to utilize excess Tech Notes from different school that you are unable to use for whatever reason into something more usable.
Like with Material Synthesis, crafting is not instantaneous, with crafting time increasing the more items you craft/convert. And like with Material Synthesis, you can use Crafting Boost tickets to speed up the crafting time to finish them in an instant.
For early game Senseis, they are very likely to be in short supply of cafe furniture, so focusing on crafting more furniture for the bonus AP and Credits boost is essential. The second priority is getting more gifts to raise the bond level of students, unlocking more of their Momotalks, giving small stat boosts, and allowing them to use their unique equipment at a certain bond level.
If Senseis are satisfied with their furniture count and gifts, then they can start focusing on other materials, like Tech Notes.