Can a malignant thymoma weaken the immune system?

Age related. In adults there is little evidence that there is a negative impact on the immune system . This in not the case in children.
See below. The prevailing thought is that the t-cell negative selection process that prevents self recognition is impaired in thymic tumors; to answer your question in plain terms- yes the immune system is impaired but the manifestations of this dont result in infections but with problems like autoimmune disorders and secondary cancers are increased;.
Perhaps. There are several syndromes associated with thymomas, some of which may lead to" weakening" of the immune system. This could also result if chemotherapy were administered as part of the treatment.