9v batteries are unlikely to work; they arent designed to supply the current to run the controller and all its accessories much less the motor.
Keep in mind that every battery / cell model has its own performance limitations.
For instance, the generic LiFePO4 cells you might find in a typical ebike battery pack will be 1C cells, maybe 2C burst for a bit, without voltage sag that could be quite significant (reducing the actual wattage supplied and heating the cells from wasted power inside them at the higher current rates).
Other chemistries can also be like that, but theyre more likely to sustain higher currents with less sag, though they have other disadvantages like cycle life, etc.
There are better cells of all the chemistries, but generally the pack sellers have no idea whats actually in a pack, and even if they say it is a certain cell model or cell specification, they dont make the packs so they cant actually be certain of that, and its usually marketing hype they post on their pages, which you cant trust until you get the pack yourself and verify by stress testing it that it does what it said it would do. Even places that make the packs themselves may lie (or not actually know what they have) about what they build with.
Theres at least a few that have been known to build using recycled junk cells of completely unknown type, lifespan, performance, etc. (they might even mix chemistries without knowing it depending on the sources of the junk cells they use).
Theres threads linked in the Sticky Index in the Battery Tech section that give more info on battery specifications and how they work, but the C rate of a cell is how much current it can supply, rated by how many times its capacity that is. So a 10Ah pack made of 1C cells can supply 10A, with some voltage sag but probably not a lot. If you tried to pull 20A from it (2C) the cells would sag a lot more in voltage (total pack voltage will drop a lot), and that lost power ends up as heat inside the cells.
So lets say its a 58v 10Ah 1C pack made of really cheap cells (for a worst case example), fully charged. While riding under normal load on the flats at a normal speed, lets assume youre pulling 10A and voltage drops to 54v, so you are outputting around 540W from the pack. Then you reach a hill, or you hit a strong headwind, and your system (say its 1000w, with a 20A controller) starts pulling the max current it can to sustain the speed, and voltage drops to say 48v (really crappy cells) under that 2C load, so now its about 48 * 20 or 960W output from the battery pack. Since it wouldve been 1080w without the sag, then there could be as much as 120w of heat being generated inside the battery at that higher current draw, and generally heat inside batteries is bad, especially if its sustained.
All that said, a 20Ah 48v (58-ish fully charged) LiFePO4 pack will probably weigh around 30lbs, maybe more, depending on how its made and what kind of cells it uses (pouch will probably weigh less and possibly perform better, while cylindrical cells will probably weigh more and perhaps perform worse (as there seem to be more crappy cylindrical cell packs out there). Itll probably be about the size of an old style metal 50caliber ammocan (which is convenient if you need something to put it in and its the right shape to fit inside one).
As for volatility--its much more about cheapness of cells and packs built from them (quality of manufacturing for each) than it is about which chemistry it is.