Hi @Beetrootlady I think it sounds like two major things have happened in everyone's life at the same time and that's really difficult.
I agree with pps that the fact of introducing your brother's new little one at an early point and at these family gatherings (which are very sad for all the adults and I am sorry for the loss of your Mum) is not likely to be an issue. As much as there is best practice, there is real life too. Your brother couldn't not be around during his Mum's death and funeral. He also couldn't be away from his new little one as they establish their bond. And it was probably quite important that he be playful and hands on even when that jarred with the funeral setting.
But it seems to me from your later posts that what bothered you most was how your brother and his friend was interacting with his little one. I think (but apologies if I have this wrong) that you feel they were being too full on and intense with her.
From what you've described, I can understand why it left you feeling uneasy. It's also unfortunately harder for posters here to comment on the appropriateness accurately because we weren't there and know nothing of the usual temperaments of those involved.
Can I ask how long your brother and sister in law had introductions for? Some can be incredibly quick; mine and my husband's was on the longer side (3 weeks before our son moved in). That for me makes a bit of a difference because typically during introductions the interactions are supervised either by a social worker or foster family. Ours would gently guide as to the best approach with our son in various situations. Guidance/best practice after all is generalized. But every child and their needs/best approach is different. So for example we spent a lot of our early interactions on a trampoline doing a lot of bouncing and my son climbing all over my husband. This first happened at our very first meeting. Our son as you may have guessed was older (5 at the time) and very full of energy. So this may not be comparable to your new niece at all. But hopefully it demonstrates that slow and gentle interactions are not right for every child.
Also, how long did the throwing, whizzing and peekaboo last? Did it start quite full on and then calm down? Or was it for quite a prolonged period/most of the day? Gently, new adopted parents typically find the process very strange and make quite a lot mistakes. Heavens knows I did and still do (4 years in). Taking things too fast is a very common one which is why you find so much advice about it. But then we all learn and adjust to our mistakes. And it strikes me as an incredibly difficult situation for your brother. Grieving his mum and trying to bond with his little one at the exact same time. I could absolutely see me going over the top trying to be happy and confident for my little one when inside I was really struggling. In fact if I think back I could probably find examples of times I was like that with my son. Hindsight is a wonderful thing. I also know I wouldn't as an adult like having a new child whizzed in my face during a wake.
Finally, and perhaps most importantly, how was your niece responding to these interactions? Was she distressed, was she showing non verbal signs like pushing them back or turning away? Or was she engaged by them? For me the key question is whether the actions were overstimulating for her. I can absolutely imagine how this would be overstimulating for grieving adults in a funeral setting; but not actually inappropriate for the child. But again, a lot depends on how long this all went on for.
In your position I wouldn't do or say anything about these specific events. Ultimately it was a very strange time and difficult for you all. Your brother may well have misjudged these events/interactions. If this is an isolated incident, hopefully any harm is minimal. It's hard to think of many circumstances more unusual than trying to establish life as a new adoptive family while saying goodbye to your own mum.
If in answering my questions above (and by the way they are intended to help you and you don't have to answer me at all) you feel your brother did go over the top here, then it may be sensible to keep an eye out for patterns. If you notice patterns starting to emerge, I would first wonder whether him being too intense could be a sign he is struggling. Either with all the new responsibility or with attaching and bonding with his daughter ('fake it until you make it' in overdrive). That might be the point at which I'd start thinking about how best you can reassure and support your brother. It will be important if you ever spoke to him about this, to come from a place of checking if everything/he is OK, rather than only looking at it from reporting what you saw and felt.