These are very smart questions.
The answers are FAR, FAR beyond the scope of what you can expect to get done right, for free, anywhere on the internet.
If you have a serious business, you need a lawyer. You need a continuing relationship; you need him or her on your speed-dial.
If you don't have a lawyer, you're not very serious about your business. Unless it's a hobby or something you're doing as a whim, it deserved to be done right. And you or anyone else in your position needs legal advice, the earlier in the process the cheaper and better. A good business lawyer will find ways to save you money, or even make you money, over time -- almost certainly far more money than you'll spend on his legal advice now. This is the classic "ounce of prevention" scenario.
I'm NOT the lawyer you need -- my practice is devoted to helping people like you clean up their mistakes or otherwise deal with them in lawsuits -- but Avvo.com is a good resource. Or I can certainly put you in touch with a colleague with whom I frequently work, and whose practice not only includes all the topics you've asked about, but a lot of others you probably aren't AWARE that you need to know about. (But you do!) Good luck!
You'll need more legal advice than what can be provided here. However, on first glance, I'm not sure I would lump real estate investments into the parent LLC. In addition, to the extent that each purpose will be operating under different names under the same LLC, you will need a dba at the least. As for separate bank accounts, it certainly sounds easier from an accounting standpoint alone.
If your different "companies" will actually be separate LLC's, then you will certainly need separate EIN's. If you will be operating any business under a name different than the LLC's name, then you must file a dba with the state and counties in which you do business.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.
I completely agree with the other comments. There is a plethora of information that needs to be obtained before any advice on the various structures can be given. As was mentioned, it is unclear from your question what business structure the other three entities will ultimately be, and dependent upon that (e.g. d/b/a, LLC, etc.) the answers to many of your questions will invariably change. The old adage, "an ounce of prevention is worth a pound of cure," is never truer than with that of business formation. You need to discuss your individual needs with a business attorney and an accountant prior to taking any action.
[Credit to B. Franklin for the above quote]