I think there IS a need to compete. You have to produce more than just subsistence. Without any goods to trade, this hypothetical third world commune will have very little economic growth.
Hence the need to be competitive with other producers in the marketplace (which could be private industry). If private industry can produce the same goods far cheaper than the commune then it's tough for that commune to make money. No/low income means there can be very little industrial build up with no funding to invest in more infrastructure, equipment or resources.
This is why I mentioned political power. Government can support that industrialization process. e.g. directly providing funds, building infrastructure, creating laws that bring foreign capital. etc.
Correct. It's wants would exceed what it can produce. It can trade the excess of what it produces for other goods and services.
Self sufficiency is difficult at a commune level. Just access to healthcare is a need.
We can see this already in real world. Don't even worry about the commune aspect. A less developed country has lower access to healthcare, education, etc. To develop they have to have something valuable to trade.