Is the president allowed to own anything as far as homes businesses etc?

Answer 1

Yes. The President of the United States is allowed to own homes, businesses, stocks, bonds, or any other kind of legal asset or investment.

However, the assets of a President Elect, sitting President, and some other politicians are often put into a 'blind trust' to be managed by others, with no knowledge or input by or to the elected official in question, to prevent any conflict of interest.

Likewise, the President will generally not directly buy or sell any of these kinds of assets while in office, as an inherent conflict of interest or undue influence would be nearly impossible to avoid.

In some cases, when some conflict of interest would be impossible to avoid, the asset might just be sold off instead.