At the beginning of a relationship, it is not unusual for contact to be more frequent and then to decrease. This may be due to the other person feeling confident that you're still interested or in not finding the need to pursue but assume a more relaxed laid back role. Of course, other individually specific reasons may apply.
If you have the sense that this is the start of a romantic relationship, then you would want to clarify with him how frequent should contact be. Is he busier than usual, is he dealing with something at the moment, etc.
When you send him a text/email or leave a phone message, you can clearly state that you hope/expect to hear back from him by such and such day/time.
You would not want to enter into a relationship without clearly defined expectations and boundaries. If he is unable to follow through, you're not obligated to wait for him indefinitely. The next time the two of you meet, perhaps you can discuss what sort of a relationship is this going to be - platonic/romantic, distant, etc.
Once you leave a message for him, it is his turn to contact you. Man are supposed to do the chasing and react in a gentleman like fashion by being courteous and responding to your texts/emails/phone calls. Even if he is busy, he could send a text saying I'm busy and will contact you at such and such time. You're not being inflexible but simply want to have an open communication and a clear understanding about what is going on.
No. Being the initiator of all of the contact is not sufficient to reflect a relationship. It takes both of you to initiate and maintain communication. You've already expressed your interest. What he thinks is not something you're in control of. If his interest is high, he'd find a way to reach out and keep in touch rather than do it randomly.
If you have contacted him and he had not replied to you in 3-4 days what would be the point of you contacting him once again? He gets your calls/texts/emails correct? If he does not contact you within 2 days of your contact, this can be an early red flag to you regarding his level of commitment when the relationship had not even taken off.