"Exar" is just the joint venture for the Cauchari-Olaroz Project in Salta between Lithium Argentina (LAAC) and Gangfeng. Your list of "not mentioned" points are all disclosed in LAAC's corporate presentation and quarterly results on their website:
"Percent battery quality of their lithium carbonate" - 0% is battery quality. They're currently producing 99.5% grade lithium carbonate; however, it has been noted that it is currently below battery grade due to the level of impurities, and requires additional processing to reach battery grade. The subsequent discount for their product is US$1500 per tonne. When added to their OPEX rate of US$6543 per tonne, you have an ultimate cost of US$8043 per tonne of battery grade lithium carbonate produced.
"Sales and/or exports of the 25000+ that have been produced vis-a-vis the lithium price" - LAAC purchased 49% production from Exar, and Gangfeng bought the other 51%. LAAC on-sold the majority (80%) of the product they had purchased from Exar to Gangfeng, with the balance (20%) sold to Bangchak. Sales would have been ~US$9500 per tonne, reduced to US$8000 for the tech grade discount, though fourth quarter declines have reduced realised pricing to US$7000 per tonne.
"Production costs and operational problems"
As mentioned above, they've disclosed their long term OPEX rate as US$6543 per tonne, plus US$1500 per tonne for additional processing to BG, totalling US$8043 per tonne of BG lithium carbonate produced. I'm not sure what problems you're hoping to hear about; they're currently operating at about 80% of nameplate, while AGY is in C&M. Their ramp up seems to have gone pretty well quantity wise, and if they can get to battery grade, all the better. If not, they just wear the additional $1500 processing cost.
It seems far more logical to operate a large scale project and pay ~US$6.5k to produce tech grade followed $1.5k to get it to battery grade, than it does to operate a boutique "battery grade" operation and require US$18k per tonne for viability. Essentially, Exar can deliver battery grade lithium carbonate for around US$8k per tonne, which is less than half the price that AGY needs.
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