There are tools like that allow you to test websites across multiple browsers in a single step without the need for installing each one individually. However, there is no guarantee that the website will look exactly the same on all browsers. Personally, I have not used these tools extensively for browser testing.
From a programming perspective, it is nearly impossible to create a website that will consistently appear identical across all devices and browsers. The more intricate your code and styling are, the higher the likelihood of encountering issues. While most modern browsers can render standard content accurately, older or less flexible browsers may struggle with complex designs. To minimize compatibility issues, it is advisable to maintain flexibility in your design (avoiding unnecessary use of position:absolute, for instance). Ultimately, minor variations in display between browsers should not significantly impact user experience.