>>5322684>buy own routerI doubt it. Your ISP will need to be able to identify you or someone could easily steal their services and they would have no way of knowing. Also, it's your modem that connects you to the internet through your ISP, not your router. Your router is for your own private network. Although they usually come as 1 unit nowadays you can buy your own router, but you will still probably need to use a modem provided by your ISP.
>How does the https prevent them seeing what they type?HTTPS is an protocol based on HTTP. It is not only end-to-end encrypted, but uses digital signing to stop an attacker spoofing the contents of a webpage, which was a common attack for social engineering.
HTTPS works with a communication algorithm called TLS (Transport Layer Security) or, formerly, SSL (Secure Socket Layer), which runs over TCP.
TLS/SSL uses 2 types of encryption algorithm, a symmetrical algorithm (usually AES), and an asymmetrical algorithm (usually RSA). In combination this allows 2 users to share end-to-end encrypted data, so no secret data is ever exposed to the internet. This is thanks to the asymmetrical encryption (which is really just multiplying 2 huge numbers together) which allows you to use 2 keys, one private (secret) key you use to decrypt information, and one public key that others use to encrypt the information. If a piece of data is encrypted with your public key, only the holder of your private key (i.e. you) can decrypt it. This means that any data sent over TLS, and by extension, HTTPS, will look like line noise to anyone sniffing packets. It is (practically) impossible for them to discern otherwise. Creating a keypair is a relatively easy process, however, cracking one (which requires factoring insanely large numbers) is not feasible with current technology. The current best known algorithm for factoring large numbers is the General Number Field Sieve. As it stands it would take aeons for this algorithm to break RSA-2048.