Canary Wharf station is a 7-minute walk away and West India Quay is just 4-minutes. The D3, D6, D7, D8, 15, 115, 135 and 277 buses all stop nearby.
There is a pay-and-display car park just behind the museum.
Yes, in the toilets in the reception hall.
Yes, the whole of the museum is buggy friendly.
The museum has a cafe on site and a popular caribbean restaurant, Rum & Sugar, where kids eat free!