Do I need to obtain any governmental license, permit, etc to operate as an individual software contractor
Software development is not normally a regulated activity (unlike selling insurance, stocks and bonds, pharmaceuticals, used cars, tattooing people, etc.) so is not subject to special licensing rules.
Many will recommend that when you start a business, you separate it from your personal finances by creating a separate 'legal entity', such as a Limited Liability Company (LLC) or Corporation (i.e. "incorporated"). This gets more important when you get bigger and are taking money from people to invest in your business (shareholders) and employing people.
The main benefit of a separate legal entity is if the business venture fails (e.g. becomes insolvent), your personal assets are not within reach of the creditors because the property of the company and your property is separate. There can be other benefits in terms of taxation and one could argue that a company looks more professional than an individual (sometimes called a "sole trader" or "sole proprietor").
However, that is not necessary. You can still operate as an individual. If you however wish to use a different name (e.g. "Acme Software") you may need to register the name with your state as a d/b/a (doing business as).
The resolution of sole proprietor appears to be a form that states you are establishing a Sole Proprietorship with a given name. I am not clear about this, but I think it is necessary when the sole proprietorship is operating under a different name.
Do I need an account different from my personal checking account, and if so, what type - personal or business?
If you want to keep payments separate (it might make bookkeeping easier at tax time) you can, but a business account is not necessary. It is necessary however if you are opening an account for an LLC.
I requested and received an EIN that I'm using instead of my SSN on the invoices sent to the company. Does using this EIN make it more likely to be required the items above, given that EIN is normally associated with a business, and SSN with an individual?
You generally only need these if you are paying other people (e.g. issuing W-2s or 1099s). You shouldn't need to put your SSN or EIN on invoices, they just need to make the check payable to you personally. However, as you are not incorporated and it is in the course of business, if the amount is over $600, your client will need to issue a 1099, and will need your social security or EIN number.