ALICE detects the conversion of lead into gold at the LHC

No, but in the Medieval days, it was a common hobby to try to figure it out, called Alchemy. They figured lead and gold were otherwise so similar, why can't you just... convert it? Because it requires nuclear physics instruments, or neutron stars. Some suspected it might be complicated, maybe impossibly so. Imagine going back to the 1500s and telling one of those guys "yes, it is possible, but it's not as simple as melting lead and mixing in some gold starter... first, you need to understand superconductors, supercomputers, subatomic physics..."

At what cost?

This is something I don't get - solar system is say 5 billions years old (a bit less I know). Universe is roughly 13 billions, and our Milky way almost the same.

What this means is that there must have been quite a few collisions of such before solar system formed, to produce so much of heavy stuff we see in our planet, no? Stars can produce only up to Fe in normal way. Yet it seems such collisions are very rare, and its not like during collision half of the mass converts to a golden blob (or more like atomic mist spreading away at fraction of c).

I know 8 billions of years is a long time, and gold once fused ain't breaking apart to H or He anytime soon, but still it feels like our planet should have way more basic atoms and not all of those rare fused oned. What about super/hypernovae?

Stars produce beyond Fe during supernova.

The other thing to keep in mind is that the early universe was filled with giant stars, these stars don't last very long. Ironically, the more fuel you have, the quicker you burn through it for stars, so a lot of supernova have happened before our solar system formed.

For additional reading, google "Stellar Population" it's about the amount of metalicity in a star based on how many "generations" old it is

With this process we could produce about 65.4g of gold with the energy needed to boil the entire ocean once to full vaporization.

The Earth's oceans contain approximately 1.4 x 10^21 kilograms of water, which equals 1.4 x 10^24 grams. The average ocean temperature is about 3.5 degrees Celsius, and we need to heat it to the boiling point of seawater at approximately 100 degrees Celsius, for a temperature difference of 96.5 degrees Celsius. Seawater has a specific heat capacity of about 3.93 joules per gram per degree Celsius. To calculate the energy needed to raise the temperature, we multiply the mass by the specific heat capacity and the temperature difference: 1.4 x 10^24 grams x 3.93 joules per gram per degree Celsius x 96.5 degrees Celsius = 5.3 x 10^27 joules.

After reaching the boiling point, we need additional energy to vaporize the water. The heat of vaporization for water is approximately 2,260 joules per gram. Multiplying this by the ocean's mass gives us 1.4 x 10^24 grams x 2,260 joules per gram = 3.2 x 10^27 joules. Adding these two energy requirements together, we get 5.3 x 10^27 joules + 3.2 x 10^27 joules = 8.5 x 10^27 joules total to completely boil the ocean. Now, for the LHC gold production calculation. The LHC produces gold at a rate of 10^-11 grams per year and consumes about 1.3 x 10^15 joules of energy annually. To produce 1 gram of gold would take 10^11 years of operation, requiring 1.3 x 10^15 joules per year x 10^11 years = 1.3 x 10^26 joules of energy. Comparing this to the energy needed to boil the ocean (8.5 x 10^27 joules), we calculate 1.3 x 10^26 joules divided by 8.5 x 10^27 joules = 0.0153. This means the energy needed to produce 1 gram of gold via the LHC would boil only about 1.53% of the ocean. Conversely, the energy required to boil the entire ocean once could produce approximately 65.4 grams of gold using the LHC process.