Short answer: as much time as you can set aside. But I'd recommend a minimum of 4 or 5 hours. There can tend to be long lines to get in, especially in high season. If you're short on time, get there early to avoid a long wait getting in.
There is a lot to see at the Louvre--you could literally spend days there--so I'd suggest researching what you are interested in seeing before you go. It will prevent you from being overwhelmed by choices when you get there. Also be prepared for huge crowds around the museum's most famous works: the Mona Lisa, Venus de Milo, and Victory of Samothrace. If you want to get close to these treasures, prepare to be patient and build in extra time.
It'll be tough. The Louvre is enormous has has many different departments. You could easily spend days in it! If you do go with limited time, I recommend the following: get the catalog ahead of time and write yourself a plan of what works you definitely want to see. I'll tell you right now: leave the Mona Lisa for last. She's going to take standing in line for a while, the girl is that popular. Make sure to hit the works/collections that are near each other, so you don't have to walk long distances. Try to go from the less famous works to the more famous, because most tourists go the other way round.
Good question! Wow. I definitely recommended you prepare in advance. They are open daily from 9am-6pm and until 10 pm on Wednesday and Friday evenings (except on certain holidays) and closed Tuesdays, so plan to go on one of the late closing days and avoid Tuesdays. Also, you will want to avoid long lines that take time away from actual art-- Use the Porte des Lions or the Metro entrances! Check out the Louvre website so you can be prepared to look at things that really interest you and skip things that are not as important. You could literally spend a week in the museum and not see everything. If you can only spend 6 hours, know that you can?t see it all-- as if you needed more reasons to visit Paris again.