>>967746If you remove this center leaf, the one that is center most, so that nothing is growing in the center, it will sprout shoots up from the soil like in your photo. I did it all the time when I had aloe plants and was eating the centers and "pups" as you call them.
>>967745Make a pot of coffee, let it cool, dilute it 1 part coffee and 1 part water, use that as your fertilizer. Coffee grounds are N2.1% P0.3% K0.3%. That is the fastest way to give them nitrogen. Make sure to check the soil acidity. Too much coffee water will make it acidic. The soil pH should be 7.0 and 8.5 for aloe. Use the coffee water once every 2-3 waterings until your nitrogen levels are sufficient using that tester kit.