First it is 1080p which is a resolution, not a density. (1080dpi would be crazy cool though!). Most displays have a density of 80-130dpi, or a dot pitch of .25mm to .29mm. TVs tend to be much larger/worse as they are upwards of .5mm or aprox 40dpi; meaning it is very large, but not detailed. Good for presentations, not so good for work. As a note, some of the highest dpi screens out right now are capable of aprox 400dpi, which is getting pretty close to being the smallest possible size the human eye can see.
Second, yes you can hook up a flat panel display to a computer; This can be done through the blue VGA cable (analogue), or through an HDMI cable. Some flat panel monitors can even take DVI, which is convenient as that is the 'defacto' standard on most computers today (VGA being the old standard, and HDMI or Display Port being the new standard). Just hook it up, right click on the background and select "screen resolution" for win7, or "properties" and then the "Display" tab for everything before vista (cant remember what Vista's is as it was odd and I only used it for a month before going back to XP), then select your monitor and whether you want to clone/duplicate, or extend your screen to it.
While this will make the image larger, it will not necessarily make the image any more detailed (unless you are currently running a laptop, or a rather small monitor). 1080p is about the lowest resolution you want to run at when doing detail work. If this is something you will be doing for the long term you will want to spend some good money on a nice large high resolution monitor. They generally last forever, and when they die it is usually an easy fix (replacing a capacitor or two). However, if this is a one time deal I am sure that the TV will work just fine.
As to whether or not you can open TIF files; it is an OS limitation, not s screen limitation. As it is a popular file type (if a bit old and lacking compression) you should have no problem opening it on a computer all the way back to 1995.