The cumulative price of Li may be small, but since once used its recycling cost is higher than its extraction cost, then as a result, the price can only grow up (except when like with oil there is strong manipulation of the market by the banks).

The beauty of a world which resources are finite is that cheap resources always finish to disappear.

More than 7000 of those cells go into a Tesla battery pack. That adds up to several kilograms of Li per vehicle!

Yes but you use more manganese or cobalt or w/e based on the chemistry of your battery than Lithium. Oddly enough if Tesla is going to buy mines for batteries Lithium most likely is not going to be their first buy. I don't know exactly what chemistry Tesla is going to end up using but if it's LCO/NMC which is 60%/20% cobalt they probably want to find a source of cobalt before lithium. If they are going to sploosh on super fancy NCA batteries (unlikely since they only do about 500 cycles, LCO and NMC are the most likely chem for EV's) which are only 9% cobalt that still probably makes sense since the world production of cobalt is about 10 times smaller than the production of Lithium.

Musk mentioned nearly the exact percentages of metals used in the last Tesla shareholders meeting recently.

Do what are they? I couldn't easily find out, I've seen various sources quoting NMC and some indicating that they are switching to NCA.

7000 * (0.3 to 0.7) = 2.1 to 4.9 kg per car.

At 400K preorders they will need 840 to 1960 metric tons of Li.

Australia alone produces 13400 metric tons per year, Chile another 12900.