Can I display a brand logo in a picture on my website?

To begin, more information is required regarding your intended use of using another's logo on your website. If it is for a commercial purpose that is associated with providing goods or services, you are likely not permitted to use what is assumed to be a registered trademark. However, if you are merely commenting on, criticizing, reporting on, or parodying the logo, you may have a defense against any claim of trademark infringement. Before including any trademark owned by another on your website, please contact an attorney who can counsel you appropriately with respect to all the circumstances.

Unfortunately i need more detail. Who's logo is it. What does the website say? What is the content of the website? Etc.

With permission from the Brand owner, yes. Without, probably not.

Short answer not without permission from the owner. There are some exceptions for news organizations, education, etc.

It depends on WHY you want to display the brand logo. If it for purely informational purposes - for example identifying a particular brand of laundry detergent - then you could show the TIDE logo. If it for any purpose that is not informational - you could get into trouble with the brand owner - if they think you are misusing the logo.