<object> tag with pdf doesn't work in firefox and is messed up in IE

Answer 1

When you deliver dubious HTML:

                                            ^      ^
                                            |      |
                                          Start   End?

... browsers try to figure out what you had in mind, with a varying degree of success that depends on the algorithms they implement and how imaginative the webmaster is. Different browsers can't always agree on how to handle valid code (where there're clear rules and specs) so it's to expect that the level of disagreement increases with invalid code.

IMHO, the simplest path to obtain cross-browser compatibility is to generate valid code. As help, you can use the on-line W3C HTML validator or whatever equivalent tool your IDE provides.