Your question makes several simplifying assumptions, which is understandable because almost every depiction of a neuron in pop culture is of a stereotypical pyramidal neuron, common in many interesting parts of the brain, which have the single long axon and big bushy tail of dendrites. But as you can see from the link, the axon also has a lot of projections on its end and indeed can connect to thousands of other neurons in different parts of the brain (in this type).

In terms of how information is relayed, that depends on where the neurons are located and what type they are. But sticking with these pyramidal neurons in the brain, the transmission, processing, and storage are all part of the same procedure as a neuron, upon receiving enough input signals of enough strength in enough time, will then fire a signal (action potential) of its own down its axon to the neurons it connects to. The storage part is achieved when many more signals come along one connection than another, the former connection is strengthened while the latter is weakened. (This synaptic plasticity has the common description of "Those that fire together wire together.") The principle of how all this works is exploited when we build artificial neural nets, as used in AI. Getting into that will get even more off-topic.