I think your question is still not complete.

1) You need to just browse images to upload, download

a) Use ADMIN/File manager

2) You need to browse images to just show an image in my page (Not editing other content)

a) Use Media module instead of text/html

3) You need to insert images along with your own text/html content

a) Use text/html module and write your content. Insert images at your desired part of content by clicking the image button

The quick upload feature is available, but you need to enable it at the FCKconfig.js (Just set it to true). This feature allows you to upload images to the root folder and there is no way of browsing images with this feature

Hope you can understand me about your incomplete questions. It is difficult to help without information.

Please explain your problem. What are you trying to browse?. What kind of user is used?. has that user permissions to that folder?.. etc.