Frankfurt Airport! Please Help! URGENT

Kay, you are distressed obviously, but realistically no one here can confirm that you and your luggage will make the connection. Fingers crossed that you do.

Yes, you are obviously very concerned but as your request is "urgent", it also sounds like you're locked into your flight arrangements. Crossing our fingers for you is about the best we can do. Put on your running shoes, and good luck!

Ask the agent when you check in for your flight if they have any suggestions?

I will hazard a couple guesses. These are based on this being one through ticket.
Lufthansa considers this a legal connection, so they believe it will work.
If your flight from Krakow is on time the distance between gates should not be a problem, as you are in A. You do need to get stamped out of Shengen, this should not take long, and you should be able to get Lufthansa personnel to fast-track you through to make your flight. The biggest issue is that your plane may not be at the gate but on the field, and thus there will be an early gate closing for everyone to be bused. If your incoming does not gate but gets bused, it is possible that your walk from the bus entrance, which is at the base of the angle for the two pieces of A(see a map) will make your walk to your gate shorter. If your incoming is going to be late, you will likely be met by Lufthansa personnel to help you.
If circumstances cause you to miss the Dubai flight, they will certainly take care of you. My guess would be that they would fly you to Munich to make the evening flight to Dubai from there, there is plenty of time for that.
Your luggage should get transferred if everything is timely, they know they have to get it to that next flight.
Should it not make it, they will certainly send ti the next day and get it to you in Dubai.
Do not plan on stopping fore food or the bathroom, even if on time. Your Dubai flight is a 747, boarding will likely start 45 minutes before scheduled departure.You can always got to the bathroom at the gate if there is time.

From our own experience we recently flew Philadelphia to Istanbul via Frankfurt. Our plane out of Philly was badly delayed due to mechanical problems that had to be fixed before it flew to Philly from FRA. We landed 25 minutes from our departure, and who knows how other people were affected. We saw the Lufthansa staff being all kinds of helpful, before we landed and on the ground, to get people to rescheduled connections or help them make their current connection.

Isn't this a question for Lufthansa? Assuming you bought this as a single flight, they are responsible for getting you and your luggage in Krakow.

Sorry: the other way around, getting you and your stuff in Dubai.

It's not worth stressing over this - either way, you will get to Dubai and even if your luggage arrives later, it's not the end of the world. I've missed a connection and just caught the next plane - I've had luggage show up the next day. Oh well - it happens despite best intentions. Bring whatever you absolutely need on your carry-on in case luggage comes later. Good luck. I've had a very short connection in Frankfurt and made it - it was a very efficient airport.

First of all, Lufthansa only uses Terminal 1, so you will arrive and depart from the same terminal.
They usually use Gates A-1, A-2, or Z, but B-1, B-2, and C may also be used.
If you check the your flight numbers on several consecutive days, you will get a good idea of the gates usually used, though that won't be a given. Frankfurt is efficient if large and luggage is handled efficiently too.

You can either type your flight numbers into Google and check Flight Aware to see the history of your flight for the past week, or look on the Frankfurt airport website. Look at the map too.
http://www.frankfurt-airport.com/content/frankfurt_airport/en/flights/arrivals.html

Do tell your flight attendant that you have a tight connection.

I flew into Frankfurt last year, my connection time was 35 minutes to Bilbao, Spain. I was totally convinced that there was no way I could make that connection, so I had resolved to myself that it was not possible and since I could do nothing, I was quite relaxed about what I thought was inevitable.
However, I made the connection with time to spare, was met by a rep. at the gate exit than taken to the passport control. Since this is part of the EU was very minimal since immigration is done at your final destination, unlike the lengthy process with a stop in the US.
I did not nothing to request any of the special expedited service, Lufthansa has figured out this connection so that it works.
But whatever happens, Panic is counter productive. It makes one prone to reacting to events that often create additional problems.

It's hard for us to determine the distance you will have to go since we don't know the flight numbers, and therefore can't find the exact gates, but using one arbitrary date, I found the flight from Krakow came into Concourse A and the flight to Dubai left from Concourse B. I made a similar connection in 2001 in 45 minutes with carryon luggage. There is a tunnel between Concourses A and B, and it should be inside security. I say "should" be because that is what the map shows, but when I did it 4 months after 911, I went through security 2 or 3 times (once at the gate itself) and still made it. You will also have leaving-Schengen passport control.

I, too, feel that 55 minutes should be enough time for your luggage to make the transfer, but, then, that's why I always carry on.