No, by the same arguments as in the previous case, aggravated by the trouble that causes to both the teacher responsible abroad and the teacher of the School. Any request to this effect should be very justified by exceptional circumstances.
You should try to avoid it as far as possible, provided that it interferes significantly with the activity pursued in the host institution. Presenting yourself for an examination in Spain involves missing the training opportunities that staying abroad entails. In any case, any absence within the teaching periods must be authorized by the International responsible person in the host institution.
Yes, if you have the authorization of the coordinators of International host institution and the ETSIT-UPM. In any case this extension of stay will mean an increase in the economic scholarship or a restriction in the number of students that can be exchanged during the next academic year.
Yes, if it has the approval of the International coordinators of the two institutions and the workload is maintained. In that case you will have to resubmit a new Learning Agreement with new courses, signed by the International Coordinator of the host institution.
Within the ERASMUS program there are institutions that take it more seriously and others less. For us (students and faculty of the School) it is serious. Insist on receiving the same treatment (and that you require) as national students. Generally there is flexibility to choose subjects that are of interest to you, but in some cases, for example in France, the juniors and seniors are very structured.