There are many reasons for these problems, including sometimes heart disease, but that would not be top of the list. Please discuss with your infant's pediatrician your concerns.

Yes

It is possible that it could be heart related, but unlikely if it is intermittent. At that age, most congenital heart problems would present with murmurs and usually poor weight gain. Sometimes there is also cyanosis or blueness that would be always present. Difficulty breathing is often airway related. I would recommend follow-up with your primary care doctor to make sure the lungs sound good and that your son does not have a heart murmur. If she/he detect any problems, then further work-up would be indicated.

Are there any color changes? Is he active? It is more common to have respiratory problems than heart problems at that age. He does need a good checkup

More importantly would be if he was not gaining weight. Your PCP might want to order an echocardiogram