Can I travel from the USA to Spain without buying a round trip ticket? What are my options? [duplicate]

Spain is in Schengen but Ireland is not, so for the purpose of visas and immigration they operate completely separate regimes.

If I would like to stay in Spain longer is it possible to leave the EU for a few days and then return to start my 3 months over?

No; the rules are not really concerned with entering or leaving; they are concerned with days that you're present within the Schengen area on. As a non-EU/EEA national without a long-stay visa or residence permit, at any point in time you need to have been outside the Schengen area for at least 90 different full days among the last 180 days.

Leaving the Schengen area for a few days does not reset anything -- except that it can help you collect a few of your 90 outside-Schengen days for later use. (Note that the dates when you leave or enter do not count as outside-Schengen).

In a perfect world I would buy my one way ticket to Barcelona now and then buy my next ticket after arrival.

The Schengen rules don't require a round-trip ticket as such. What they require is that you demonstrate that you can afford to live and eat during your stay and then also afford transportation out of the area afterwards. Having already bought a ticket is a simple way to demonstrate the latter of these, but if you can show you have enough money to buy one later, that will also work.

However, you must still demonstrate at the border that you have plans for your stay that is actually legal.

You mention in your question that you are a circus artist. You should be aware that being allowed to enter for a short visit does not entitle you to work during your stay. If you want to work, you must generally seek permission from the particular member country you want to work in, according to its national rules.

If the border guards suspect that you intend to work during your stay without proper permission, you can be refused entry, no matter what your further travel arrangements are.