how large websites find and sort data

here is a thing,consider a very large website that holds a load balancer M web servers and N database server,

a given user in this website has big amount of data that is spread across the N databases servers,user A

so if we would like to examine how the websites serves such a user then many programing problems appear,

first problem is : if the database servers that hold user A data are full then how the website automatically starts storing data on a new database server?

second problem is: how the website keeps track of all user A data,because consider that we wana show all of user A data on http request,then how the website finds all user A data from the given N database servers and displays it?

third problem is:consider that the websites offers a simple search function that finds records of data by a given factor and sorts the result to be displayed,then how such a search function works,how is it able to run across all of the N database servers and fetch relevant data and eventually sorting it by the given factor,i.e not only that we will have to find all matching data on the N database servers for the user but also we have to take the data on sever 1,server2, ... , server N and combine it then sort it,how is that even possible?

any answer to any problem is accepted,please dont vote this down so other not get a bad impression because i want others to read it and try to answer,

thank you