Equation labelling - automatic updating and format change

Question

I am currently writing my physics bachelors thesis and it is the first time i have written a document in latex. I have two questions:

1. The current document class is article, i have partitioned my thesis into sections and subsections. I have many equations in the main body which i reference in my explanations etc. As it stands, the equation label is up to about (200), and this is ugly to write everytime. I would prefer if i could number the equations by section and then by order, for example the 10th equation of section 3 (which might be located in subsection 3.2, for example) should be labelled (3.10). I know i can do this with the document class book, but i dont like the chapter style of this class and much prefer the section/subsection style. How might i get around this without manually labelling every equation?

2. I, like many other authors, did not start writing my thesis in chronological order. I instead started in section 2, then jumped to section 4 etc. Now i would like to write section 1, but i made the rooky mistake of not implementing automatic updating in my equation labelling. So for example, if i go to add an equation and label it (1), the label of every equation coming after it gets its number increased by (1). The problem is that in my (already written) explanations i have referenced equation (1) which has just become equation (2). I realise that the only way to rectify this is to go through and do it manually, but for the future how does one implement automatic synchronizing of the equation labels and equation references?

I would prefer answers for 1 and 2 which are compatible, if possible. Thank you!