My heart started beating weird for a minute. Is this what they call an irregular heartbeat?

It can be. The sense of an abnormal heart rhythm (also known as palpitations) is frequently secondary to an irregular heart beat, or arrhythmia. Sometimes individuals have this sensation when the heart rhythm is not irregular. If there is any concern, an ECG recording at the time of symptoms, using an event monitor, will usually provide an answer.
Maybe. It depends on what you mean by wierd. If the pulse became irregular, then yes. If you just felt a fluttering in your chest, it could possibly have nothing to do with how your heart is beating or your heart could be beating fast and/or strong but regular. An EKG or having a doctor time your pulse would give the answer.
Possibly. Should see doctor and have him checked.