1. Yes. Any Immigrant (LPR or Lawful Permanent Resident, i.e. Green-Card Holder, which includes you as a "Conditional" LPR or CPR), has the right to live and work anywhere in the United States. As any other student in the U.S., you can attend any university that will take you and that you can afford to attend. The individual universities will have their own criteria for admission and tuition rates. One needs to establish a residence somewhere in the U.S. as it will likely control how the university will determine if one qualifies for in-state rather than out-of-state tuition.
2 & 3. Immediately upon arrival in the U.S. on your EB-5 Immigrant Visa, you will be processed at the port-of-entry (POE) (usually an airport). At that moment, your visa is validated and stamped and will act as a temporary green-card for a year. In reality, your plastic card will arrive usually in less than a month (and so will your social security card if you checked the right box on the visa application).
IF you need to return back to the home country in order to attend to business or personal affairs, you can safely do so for up to six months and not endanger your status. IF you need to stay longer, be aware that after you are outside the U.S. for six months, you will be "seeking admission" and can be found "inadmissible" like anyone else IF you do not have a re-entry permit. Also be aware that IF you remain abroad for a full year at one time, your green-card will not be accepted as a travel document and you have to apply for a Returning Resident Visa (SB-1) from the State Department abroad.
You can make your life easier and apply for a re-entry permit (REP) while in the U.S. upon the first Immigrant Visa entry. The form I-131 is used and may only be filed while you are inside the U.S. (that is more than merely mailing it---USCIS has to accept it while you are inside the U.S.). The REP requires you to appear for biometrics (photos, fingerprints, and signature). USCIS will send you an appointment notice in 2 to 4 weeks after filing. (Once the I-131 is actually accepted by USCIS, you may depart and then return for the biometrics if you cannot simple wait around.)
An approved REP let's you remain abroad for up to two full years and NOT lose your green-card merely due to such a long absence. What you do abroad MAY cause you problems. Certain actions may make you inadmissible or be viewed as a sign of abandonment of LPR status, even if you have a REP. The REP does NOT protect your naturalization eligibility. Extended absences prolong the wait before you can file for naturalization.
However, while naturalization eligibility is something to consider up-front, it would be irrelevant if your conditions do not get lifted from your initial LPR status. This intermediary step will entail filing an I-829 and proving the job creation and full investment.
Upon receipt of the Conditional Green Card, the investor, spouse and minor child can work and study in the US. They should plan to be in the US generally a minimum of at least 6 months a year. If a child is in school, it’s best that he/she completes the term of school in the US.