Hi
@KBanana I will give you my thoughts on each of your questions in turn:
1. With busy supervisors, how often should you try to speak to them in a day?
The first thing to point out here is the obvious fact that supervisors are also human, and thus prone to inappropriate reactions and mistakes, particularly when under a lot of stress. The experience you have described could in part be explained by the supervisor's resentment with a senior lawyer making him change his approach. Unfortunately, this kind of potential reaction is a factor you cannot completely control. People can be emotional and act unpredictably, and sometimes this results in unfair consequences for others.
Nonetheless, there are some things you can do to reduce the likelihood of this situation reoccurring. To then address the point of your question, I think it is crucial to read the room and have a flexible attitude. There is no set number of times you should try to speak to them. Whenever you return to the office after a longer period of time, you can just say hi and see what reaction you get. If the supervisor quickly mutters a greeting back and then returns to work without saying anything else, you should assume they do not want to speak more and should respect that. In my vacation schemes, I had days I would have maybe one 2-3 minute conversation with the supervisor and not interact further. However, I ended up receiving positive feedback from them.
2. Is it better to wait for them to approach you/check in instead?
Once again, I think this largely depends on the intangibles of their situation and your dynamic, although you can also try to address this directly when you first meet them by asking what they prefer.
3. How many tasks would you typically be expected to complete in a week?
There is definitely no set number for how many tasks you should complete, and for good reason. Some tasks may take a few days to an entire week, while others could be completed in a few hours. At the same time, some departments will be a lot busier than others and thus have many tasks you can get involved in, while some will not. Similarly, some practice areas have more tasks that vacation schemers can attempt to complete, while others are more technical and have a higher requirement of prior knowledge.
My advice here is to simply seek to keep your schedule busy and not overextend yourself. As long as it is clear from the nature of your tasks/your conversations with people in the department that you have done your best to do what you would be expected to as a trainee, this will not be an aspect that will hold you back in terms of conversion.
4. If your supervisor doesn't give you tasks, how long should you wait before asking others?
Like many other things, I think this is an issue that you should discuss directly with the supervisor themselves, as different people will have different preferences and different firms will have different policies/cultures. You should also ask the supervisor how they would advise you to go about asking for work - presumably, they will advise you to ask in a manner that does not raise eyebrows.
This touches upon the final matter I wanted to discuss: when you go asking others for work, you need to ensure you do so in a way that is least likely to reflect negatively on the supervisor. Thus, instead of saying something like '
Do you have any tasks I could help with? My supervisor is quite busy so they couldn't involve me in any of their work' (which suggests your supervisor is not doing their job well in managing you), you should say something like '
I have some capacity left - so I wanted to ask if there are any tasks I can help you with?' (which sounds a lot more neutral).