1) Who determines its value? Markets? What kind of markets? Big companies like blockchain.com ?
The first thing to know is what gives the Bitcoin value? There is no one controlling this and it is decentralized? Well, it is related to supply and demand. The supply of Bitcoin is limited, only 21M. It is also not all that is in the circulating supply, only some of them. Moreover, some of them are not mined yet, so, the supply right now is so limited. While on the other hand, the demand for BTC is exactly high. Moreover, in this technology era, many people are willing to put their money in BTC because of its interesting and promising characteristics. In fact, many more people want BTC. The supply and demand will always be there, more demand, the price or value will be higher.
However, as we know that the price of the BTC is very volatile. It depends on the market, yeah. The price depends on the market, and it is stated that there is no one can control the price of the market. Probably true that somebody may not be able to control the price in the market. But, what about some people who have a big amount of BTC that play the market? It is possible to influence and control the market of BTC.
How is it getting embed on websites? If you google "bitcoin" you will see its price. This number must be set by a person, right?
If you are talking about the display of the Bitcoin price on google search, there are some parties that provide the data. The price on google search for USD rate is by
"Morningstar for Currency & Coinbase for Cryptocurrency".
You can also find such kind of Bitcoin price and market tracker on some tracker websites. They are such as Coin Market Cap, CoinGecko, and others.