What is the limit of electrical outlets that I can connect using a 15 Amp breaker?

No limit for residential.

But, if doing it, wire nut the splices in the outlet box and pigtail to the outlet itself. It's not mandatory, but it's safer and harder to do.

It's actually mandatory for the Neutral.
I would also pigtail both.

Obviously it's more important to know the load you will plug into the outlets rather than the number of outlets. Can you tell us what you are planning?

It's actually mandatory for the Neutral.
I would also pigtail both.It is not mandatory to splice the neutral unless it is part of a multi-wire circuit where both circuits are present in the box.

Obviously it's more important to know the load you will plug into the outlets rather than the number of outlets. THIS is key. :)