Bitcoin Faucets are a way to give out free bitcoin, the aim being to increase the popularity of Bitcoin (or other Crypto Currencies)

As Bitcoin has increased in value, less and less people are willing to just 'give away' what is becoming a valuable commodity, so Faucets are becoming a less common sight, and the ones that do still exist usually require some form of interaction in exchange for free BTC.

freebitco.in is one of the few legitimate Faucets remaining, and it is possible to earn a few Satoshi's every hour, which eventually add up to a usable value.

As of December 2020, realistically, it is impossible to mine Bitcoin with a standard PC or Laptop, so free Bitcoins are no longer a realistic proposition for most people. Other Cryptocurrencies such as Dogecoin, Litecoin or Ethereum may be more sensible mining options.

BTC simply stands as an abbreviation of the word Bitcoin, in the same way that USD is an abbreviation of United States Dollar

A Satoshi is the smallest possible unit or 'fragment' of a Bitcoin, 0.00000001 of a Bitcoin = 1 Satoshi

As Bitcoin increases in value, an individual Satoshi is becoming increasingly relevant as a reference value, it is likely that smaller transactions will eventually be expressed in Satoshi rather than BTC, much as we currently refer to Pounds/Pence or Dollar/Cent as comparable values.

The fact that BTC runs to 8 Decimal places makes expressing smaller amounts of BTC difficult, ie .0.0000010BTC can be more easily described as 10 Satoshi.