Hi doshspy,
Most of your questions are answered in post #1 here which has all the basic information, steps, and guidelines that can help you make the best possible choices.
For the ones that aren’t specifically answered there …
No it’s not necessary although there are pros and cons to both one sided and two sided latex mattresses depending on the design of the mattress. You can read more about the pros and cons of a two sided mattress in post #2 here and in post #2 here.
Probably yes. You can see an example here of a single layer firmer latex mattress that was used for almost 50 years here. You can start with a firmer version that is suitable for growing children and then add a topper when they begin to develop more if they need some extra softness at that time. Some of the more informative threads in the forum about mattresses and children are linked in post #2 here.
Springs are more susceptible to damage from “shock” forces than latex rubber which has no wires that can bend or take a set if they are compressed suddenly.
Some of the better options in the DC area are listed in post #2 here. As far as the time it takes that would be very individual and would depend entirely on where you were, which retailers or manufacturers you visited, how specific your needs and preferences were, how much comparison shopping you wanted to do, and probably as much as anything on the amount of preliminary research you did both on mattress materials and on the local retailers in your area or online.
For many people who chose the places they visited carefully it would be enough but for some people it can take weeks or even longer.
Phoenix