Some settings you might want to look into to solve your problem. 1) You have write access to the site. 2) No one else is using the same file. 3) Check your library settings. Such as do you have to check out a file to edit? 4) Are there any pop up boxes when you open your form asking you to read or edit. When opening a form from a relevant documents site feature we have to click open as read only for the form to open properly and then it allows us to edit it, which is strange. 5) Check the settings for how you published the form. Maybe re-publish.
For your second post regarding the speed issue when opening forms. If you are running windows 7 this may apply. I moved one user to windows 7 and noticed that infopath forms took a long time to open from our sharepoint site I cannot find a link to a search result I found but it solved the problem. Do some web searches and you should find a post with several different items to try including Disable autotuning, Remove Remote differential Compression, Remove IPv6, Clear DNS Cache, Modifying Link speed and duplex values in the network adapter properties.