[RPG] How does one go about making or acquiring a physical totem object, which is necessary for the “Totem Spirit” ability

From the Player's Handbook, page 147, in the descriptions of weapon properties:

Heavy. Small creatures have disadvantage on attack rolls with heavy weapons. A heavy weapon’s size and bulk make it too large for a Small creature to use effectively.

Carrying capacity has no effect on your ability to use heavy weapons without disadvantage. That's determined solely by your size, and since this effect doesn't change your size; no, you still can't wield those weapons effectively.

Yes, you can have different totem animals for different level abilities.

Though few people discuss multi-totemed Barbarians, this is the RAW of the class's wording. Consider the 10th level ability, Spirit Walker:

At 10th level, you can cast the commune with nature spell, but only as a ritual. When you do so, a spiritual version of one of the animals you chose for Totem Spirit or Aspect of the Beast appears to you to convey the information you seek.

(emphasis mine)

This quite unambiguously conveys the idea that you can make different totem choices at different levels, and that they do not have to agree.