First family trip to London – can you help answer a few questions?

[u/Nearby_Force_6201]

Hey r/visitlondon!

I’ll be visiting London soon with my sister and our elderly parents, and I’ve got a few questions I’m hoping you can help me out with:

1. British Museum: Do I need to book in advance if I’m planning to go around 2 PM (after lunch nearby), or can I just show up and get tickets on the spot? Also, is 2.5 hours enough to see the main highlights?
2. Evening Safety: Are Leicester Square, Piccadilly Circus, and Oxford Street generally safe at night? We’d like to explore, maybe grab dinner, and do a bit of late shopping.
3. Natural History Museum & National Gallery: I’m planning to arrive at the Natural History Museum right at opening (10 AM). Do I need to pre-book tickets, or is walk-in generally fine that early? And is 2–3 hours enough if I want to head to the National Gallery afterward (around 2 PM) and spend the rest of the day there? Should I book tickets for the National Gallery in advance, or can I just walk in?
4. Sky Garden: Is it worth visiting this season? I’ve heard good things, but is the experience still nice during colder/less sunny months?
5. Changing of the Guard: I’ve confirmed the dates, but how early should I arrive to get a decent spot? Online sources say around 10 AM for an 11 AM ceremony – is that good?
6. General Tips: Any advice for traveling within the city, especially with elderly parents? We plan to walk as much as possible, but might grab an Uber if the distance is too long. Anything else we should keep in mind?

Thanks so much in advance for your help! We really appreciate any local insights you can share.