What does halacha say about the "speed" of prayer ? I know that Amida has to be said slowly enough to pronounce every word correctly but what about other prayers ? In my congregation there are sometimes people who literally skip some lines or whole prayers (the beginning of shachrit, about offerings, in about 1-2 minutes). Is it allowed ? What should I do to say the prayer correctly but to keep up the speed of the congregation ?

Your question has three parts. 1. What is the proper speed to daven? The speed at which you can pronounce all the words and understand what you are saying (if you understand Hebrew). Each word does not have to be articulated clearly, one fulfills the mitzvah if there is some slurring, but this is certainly not the best way. 2. What to do about a sheliacvh tzibbur who does not pronoune - or even skips - words. There is usually not much you can do. A Rabbi should instruct his congregation about the importance of clearly saying the words, but sometimes there are congregants who are unable to do so and insulting them may cause estrangement from the community. This is a difficult problem which requires much thought and understanding of the case at hand. 3. If you cannot keep up with the congregation, some parts of psukei d'zimra can be skipped (and made up later) sometimes it helps to start a little before the congregation, sometimes you will miss kedusha. If dovening a bit faster will solve the problem, try to speed up, but usually this is not the sufficient. The gemarra says that Rabbi Akiva, in shul, was the first one to finish the Amidah, but at home, he dovened for an exceptionally long time. Apparently, the value of communal prayer overrode Rabbi Akiva's personal wish to doven slowly. I'm sure that even when he dovened quickly he said every word.