Yes you can buy a house without a DNI but the sale will be in US Dollars and you will have to "prove" the origin and "legality" of the funds before you will be allowed to transfer them to Argentina.
It is almost impossible to rent a house (or an apartment) without a providing a guarantee of another property and many landlords will only accept a property (for the guarantee) that is owned by a close relative.
If you intend to live in Argentina more than six months of the year you will need to get at least "temporary" residence. There are many thread on that topic in the archives of this forum.
You can use keywords to find a great deal of information on many topics using the search feature and you will learn more in a few hours that you could in a few weeks if you wait for other members to answer your questions.
Unfortunately, most of the members who have posted here in the past are long gone.
PS: If you can't qualify for temporary residency don't even think about trying to stay as a pseudo-tourist (aka perma-tourist). Ignore anything you read that indicates making "visa runs" to Uruguay to continuously renew your 90 day tourist visa is acceptable. Those days are over.