In spanish "haber" y "tener" son verbos distintos. Cuando hablas de posesión, nunca utilices haber. When you talk about possession, never "haber". Cuando hablas de un deber, en algunos casos se puede emplear haber. When you talk about obligation, sometimes you can use "haber". Less common. Ejemplo: Tengo muchos problemas. (Nunca haber) Tengo que irme. También posible: He de irme. Quizás con haber denota menos fuerza en la obligación. Maybe with "haber" shows a weak obligation.

No, they're not interchangeable. Tengo una manzana = I have an apple. Hay una manzana = There is an apple. If you change 'have' for 'to be', then the concept looses its belonging relationship. REF.: I'm a Certified Spanish Teacher

"Tengo" is similar to To have." "Haber" is more near to impersonal form "there is", "There are"... , usually "haber" is a auxiliar verb, and we use to made the past, "Yo he tendio". But some time we use this alone, "Habia una manzana", "Hay una manzana", in this form never use subject.