For shorter/less substantive work experiences (say, a Forage course) I think a few sentences describing the nature of the main tasks you completed will suffice. For longer/more substantive experiences (say, a part time job or internship) I think you would ideally use the STAR structure: describe the situation of the job (how you applied, context etc), tasks you were assigned, actions you took to complete them, and any results in terms of feedback or performance metrics. I would also sparingly make some inferences as to skills this demonstrates.
As for your other question, I think you can connect the experience with the firm, especially if there are any overlaps with your 'why the firm' motivations or the firm's USPS. However, I would only do so where there is a natural way to connect the two instead of pulling at straws. The other point I wanted to make here is to be mindful of how you make use of the work experience in application form answers to avoid being repetitive.
For your use, I copied here one of my more substantive work experience answers I used in one of my successful applications. I did not make use of the full STAR structure because I already explained the context and my feedback in one of the application form, but I thought the example may still be useful:
During my one month at X firm, I mainly worked in the Litigation and Corporate departments. In litigation, I gained experience in complex cross-border disputes by conducting extensive legal research into the validity of choice of court clauses, workplace discrimination and fictitious accounting. I also honed my public speaking skills by preparing and delivering a 30-minute presentation in front of the entire firm. Together with a fellow intern, I discussed the cases in which a lawyer can be legally obligated to testify as a witness against his own client.
In corporate, I improved my attention to detail by researching and then drafting client emails about the validity of powers of attorney issued before a change in a company’s management. I also enhanced my understanding of complex M&A deals by conducting research on the legal implications of a subsidiary acquiring the parent company with a consequent reduction in share capital.
Finally, I developed my organisational skills by completing cross-departmental tasks, such as sending weekly emails to the entire firm with a summary of recent legislative and regulatory changes for each practice area.
