I'm trying to make a DFD for this scenario: after admission, the patient gets the service he needs.
I've been trying to do it using this diagram (there are 3 available services):
but I don't think it's going to work like this, maybe there is a way to avoid condition at the first place?
and how processes should be numbered in this case?
Dataflow diagrams are not as powerful and standardized as UML activity diagrams; there is no notation for conditions.
The usual practice would be to have three outgoing dataflows, that each describe the data that the Admit process could send to each of the subsequent alternatives. Perhaps only the patient id. Perhaps nothing, but Admit stores customer records in a datastore, and the others read the customer data from the datastore. If admission doesn't collect all the data, it might even be necessary to link external entity Patient to the other processes as well.
Typically, the conditions would be described in the documentation of the first process, clarifying when it will send the data to the other processes and under which conditions (outside the diagram).
About the numbering, it's not representing the chronology. It's not like an uml communication diagram, where you would use numbering for sequential chronology and letters for the alternatives. In a DFD, the processes are uniquely numbered at one level (and the next level takes the numbering of the previous level as prefix to build a unique id according to the decimal numbering).