Is a sarcoma an fast growing tumor and a carcinoid a slow growing one?

It is different. Sarcoma is a soft tissue/bone cancer; carcinoid is a neuroendocrine tumor. They both are completely different disease. Soft tissue sarcomas grow at various rates depending on the aggressiveness of the - could be presented with as fast growing tumor or slower growing process. Same thing with carcinoid- it can be presented as a slow growing tumor or more agressive one in high grade carcinoid.
Not necessarily. There is a huge variability within sarcomas and within carcinoids. Within sarcomas there are some very aggressive varieties, and some very slow growing ones. The same is true for carcinoid. So unfortunately you can't make that generalization without knowing some more information.