Absolutely nothing wrong with you attending service with her if that is what is best for her. If you think she will be okay and has friends who are attending, then you might want to let her go on her own and let her know that it is okay to take a break to get a drink of water, use the bathroom, etc.

Jewish person here to add that synagogues are used to seeing lots of different types of B-Mitzvah guests and, I would hope, kids in their own congregations. I would hope none of the rabbis would act shocked or be rude if your kid went to the bathroom a lot or whatever. I think it's fine if you want to accompany. I also personally think it's fine if your kid reads a little underneath the prayer book. Bring a purse, and snack in the bathroom. They wouldn't be the first! These things having boring spots even for Jews who have been going to temple their entire lives!

-Gift at the reception. A lot of debate on DCUM but in my experience it's almost always money (cash or check, multiples of 18 is a nice gesture but not necessary). This does seem to vary by community and whatever you choose to do will be appreciated.

-ceremony can be long -2 1/2 hours. Many people don't come at the start time and instead closer to the middle when the child will be more involved. If you're comfortable, you can ask what time that might be. It's not wierd at all for you to attend the ceremony. The more the merrier to celebrate the child, and it's a nice way for you to get a better understanding of what it's all about. But of course that's not required.

-Yes, the congregation is quiet more of the time other than singing along if they know how. My daughter who is 8 but struggles to stay in one place takes a million bathroom breaks. And I see some older kids reading books. It's not the most polite thing to do, but it's not the end of the world either. They should put the book away while the bar mitzvah of their family is leading. And they should stand and sit along with everyone else.

Others have mentioned more modest attire at the ceremony and covering shoulders. The same usually doesn't apply at the party.

It can get LOUD at the party. Imagine a wedding type party filled with young teens and their music. Ear plugs or headset would be fine if she needs. My 8 yo often has to leave the room, and depending on the venue, there's often a lobby/lounge area to get some quiet.

Even if the adults have a plated dinner, the kids usually have a kid friendly buffet of burgers and chicken fingers etc.

My ASD kid is a member of a synagogue (liberal) and has been to two of these although did not become a bar mitzvah.

Kid was invited but we stayed for the ceremony. He was super bored. 2.5 hours. He went to the reception himself for one. My partner accompanied him to the other. Was just going to drop him off but they begged him to stay because they had way way too much food.

Not enough food seems like a bizarre outlier in my experience.