It depends on what the copyright owner allows you to do. You will certainly need to do some research to find out and it is not advisable to use the image before doing the research. The owner may issue a licence, for which you may have to pay a licence fee. Please do not use any image without first finding out if your use is an infringement of copyright as this can have serious consequences and some of the biggest image houses carry out searches for illegal use of their images.
It depends, essentially this is a matter of what was agreed at the early stages of the negotiations over the production of the website and the contract which exists between the parties.
You also need to be aware of implications of ownership of the copyright of the creative work and any images used as well. The designer needs to be correctly licensed for the use of stock images and fonts.
Bear in mind that you are absolutely responsible for the compliance of your website. If you use it for ecommerce you need to be especially vigilant that you are not breaching legislation. This is particularly so when making sales to consumers. You may like to have our Website MOT to find out how compliant your website really is >read more…
There is absolutely no reason why this should be a barrier to obtaining a Trade Mark as long as the designer:
holds the correct license from the typeface font owner for the use to which you want to put the logo and
has been provided the logo incorporating the typeface font to you in a non scalable format
You are not seeking to Trade Mark the font (the designer of the font has probably already done this) you are seeking to Trade Mark the logo incorporating the font.