Manchester to Sheffield and back in a single day

Is it possible to make a day trip from around 10-11am from Manchester to Sheffield and return to Manchester (hotel near the airport by 11pm or 12am?

Manchester to sheffield and back on a day by train is easilly doable. Heck I know someone who does it as a daily commute.

Most of the time there are two fast trains per hour between Manchester Picadilly and sheffield. One run by transpennine express and the other by east midlands trains. The transpennine express service comes from manchester airport, the east midlands service comes from liverpool. Both services run through stockport.

Note that there are also slow trains from manchester to sheffield run by northern, you generally want to avoid these.

The travel websites says it's around 2-3 hours from Manchester to Sheffield (is that true? is it any longer/shorter?

I don't know what website you are looking at but national rail enquires )looking for tomorrow morning gives 1h 13m for the transpennine express train. 1h 28m for changing at manchester to pick up the east midlands train and 1h 23m for changing at wilmslow and stockport to pick up the east midlands train. Return in the evening seems similar up to 20:31 , after that there are still trains but they become slower and more widely spaced.

Note that the east midlands trains service will depart from platform 13 at picadilly. So if you arrive in the main area of the station and want to minimise your walking and avoid the crowds you should head to the over-bridge not the main concourse (you can find a station map of picadilly at http://www.nationalrail.co.uk/SME/html/NRE_MAN/plan.html?rtnloc=MAN ).

The last train back seems to leave sheffield at 22:48 to arrive at the airport at 00:50 after changing (with a half hour wait :( ) at picadilly.

Is there a daily ticket that one can buy for a manchester-sheffield and return trip?

There are several types of ticket you can consider (ordered here from cheapest to most expensive).

1. Advance: These are the cheapest option but they lock you in to a specific train and have to be bought in advance (I think it's usually the day before but i'm not positive on that). Prices vary and there may be no advance tickets left by the time you come to book. Advance tickets are always singles so you will need to buy seperate tickets for the outward and return journeys (websites will generally sell you both in one transaction).
2. Off peak day return (formerly known as the cheap day return): These are not valid before 9:30 AM on weekdays (they are valid at any time on weekends and bank holidays) and on some routes there may be additional restrictions around the evening rush hour. There don't seem to be any such evening restrictions on manchester airport to sheffield. Return travel must be on the same day (I think a couple of hours after midnight still counts as the same day). This will cost £23.50 for manchester airport to sheffield and back.
3. Off peak return (formerly known as the saver return): Restrictions on these varies heavilly by the journey you are making. Sometimes (and this seems to be the case with your journey) there don't seem to be any restrictions at all. Return has to be within one month. This will cost £29.90 for for manchester airport to sheffield and back. This is likely the best choice if you need to travel before 9:30 AM of if you are not sure you will return the same day.
4. anytime return: This is valid at any time of day and will cost £35.60 for manchester airport to sheffield and back. I think return is within one month but i'm not positive on that. I don't see any point in buying this for your journey since I can't seem to find any trains for which the off peak return is not valid.
5. First class anytime return, this woudl cost £64.80 for manchester airport to sheffield and lets you travel in first class. This is probablly a waste of money, first class on the transpennine trains is only barely nicer than standard class and the east midlands and northern trains don't have it at all. The one time it may be worth considering is if you have to travel during rush hour on a transpennine train as first class is likely to be less of a sardine can than standard.

On some journeys in the UK there are different tickers for different routes/operators but that doesn't seem to be the case here, all the off peak and anytime tickets i'm seeing are route "any permitted".