Yes. Or at least, Brits are more likely to use RARER (not necessarily longer) words. If you look at this spreadsheet https://corpus.byu.edu/100k_data.asp?query=1 you'll see that the COCA (American English) column generally has higher frequency rates than the BNC (British English) column for the 5000 most common words in English. For rarer words, the BNC column usually has a higher frequency value (Of course, there are many exceptions). The difference is not large, but it is consistent. There are a few reasons for this. Part of it is the Cult of Hemingway--American schoolchildren are actively taught to avoid unnecessarily florid vocabulary.

No. In fact, we shorten words in ways that AmE speakers don't. 'Brolly' for umbrella, 'cardi' for cardigan, for example. AmE also tends to invent words which seem ( to us at least) unnecessarily long - 'burglarize', for example. Nor is it true that BrE is more formal than AmE. Take subjunctives, for example. BrE speakers, even in formal situations, will happily use an indicative mood where a subjunctive is required. ('They insisted that he leaves' rather than the correct 'They insisted that he leave', for example). This sounds horribly uneducated to the (educated) American ear.

The wikipedia page is good, the other one isn't. The fluentu.com page has quite a lot of incorrect information about BrE. Don't believe everything you see on the internet!

I wouldn't say British speakers use larger words than Americans, but it does seem that Brits tend to speak a bit more formally than Americans. Both countries have a wide range of native speakers with different accents and speaking patterns. Some cultural groups will use certain vocabulary that to the trained ear can be easily picked out and give clues to the speakers place of origin. https://en.wikipedia.org/wiki/Comparison_of_American_and_British_English https://www.fluentu.com/blog/english/differences-between-american-and-british-english/