The short answer is yes. You can get a lot of more in-depth answers by typing the title of this thread into a search bar.
Yes. Use common sense, a good firewall and malwarebytes.
Yes. A few of the common culprits are hijacked or malicious advertisements, drive-by downloads, and hacked websites.
Cybersecurity works in layers. Having a scanning tool such as Malwarebytes Free, Kaspersky Virus Removal Tool, Comodo Cleaning Essentials, etc. is one step. Browser extensions like uBlock, NoScript, HTTPS Everywhere can help on the browser side. There are also a ton of high quality free antivirus programs such as Bitdefender and Avast that provide real-time protection.
Yes, Virus, Malware and so forth can come from websites
Yes. Run a Malwarebytes Scan (download Malwarebytes, the scan tool is free) if you are unsure, then check installed programs to find if anything unusual is there. You most definitely can get virus from websites, especially if they are download sites (those tabs that open and shut instantly as you download something).
Please, read this. It also contains a link to this video where they demonstrate that opening a web site can force your PC to execute some code (in their case, open Windows Calculator).
Always assume you can get a virus from somewhere (even on your own computer).