Hi!
In most cases, not having attended events or open days with a firm won't disadvantage your application - I hadn't attended open days or events with the firms I did VS' with or the firm where I have a TC! The graduate recruitment team know that places are limited (and often very competitive!), and that not everyone has access to them. What matters far more is whether you can articulate genuine interest and understanding of the firm through your application, regardless of how you got that insight. If you have attended a firm's event, it can be nice to reference it briefly if it informed your motivations - however, it is absolutely not expected, and I would definitely avoid using it as a tick-box exercise.
As for listing events with other firms, I would say that it is worth including them if they influenced your wider motivations (e.g. it sparked an interest in a practice area that relates to the firm you are applying to), or if the application specifically asks about them. However, if you feel it doesn't add any actual value to your applicaton, it is completely fine to leave them out. Your space is often better used showing why you are interested in this firm, rather than displaying the wide range of events you have previously been to.
As long as you can show that you have researched the firm and have clear motivations for applying there, you are not missing out by not having gone to any of their events