Let me answer the first part. Yes you (and if you have a spouse or children) are given a conditional green card/LPR/I-551 (valid for 2 years) after your I-485 AOS (Adjustment of Status) is adjudicated. Once your case is adjudicated you gain Lawful Permanent Residency, and yes you can live/work/register a business/travel and also apply for most benefits reserved for US Citizens (barring voting, jury duty, Federal Govt. Jobs which need clearance which requires you to be a US Citizen, etc.). You have 90 days before your conditional LPR expires to apply for I-829 to remove conditions. Once you file the form, and get the receipt you make an appointment with your local USCIS office to get your passport stamped for I-551, so that you can prove you are still a LPR albeit currently waiting for conditions to be removed.
Now to your second part, yes you HAVE to show USCIS you have committed to a project (New Commercial Enterprise) managed by a regional center or in the case of a direct investment, to provide proof that you have invested money in an NCE. Remember, you have to show a signed contract and bank details of wire transfers providing proof of your commitment that you have transferred the required capital towards an NCE i.e. you have transferred the principal capital into an escrow account. During the filing of your I-526 case, you need to SHOW bank records (dating 5 years) that the principal you invested was lawfully attained and transferred (i.e. to an escrow account which will later be used to fund the NCE). Until your I-526 is approved your funds sit in an escrow account. Once the I-526 is approved, the bank which manages the escrow, transfers the principal to the regional center, and in the case of a denial the principal is returned back to you. Merely showing proof that you "have funds" for investment is impossible as you can't even fill the I-526 form without details of the NCE or the Regional Center.
Please note, I am not an immigration attorney. I am just an investor, so I would strongly advise you to contact a reputed immigration law firm who has business attorneys who handle such kind of cases. Eb-5 is an extremely complicated process, and I would suggest that you get the right advise from the right people before making a decision. You can PM me if you want, I can get you in touch with a due diligence firm that handles and provides economic reports about EB-5 projects. They will also "vet" you to see if you are an accredited investor. I strongly suggest you do that before contacting a regional center.