Minecraft Better Together Edition/Minecraft Bedrock Edition is basically the continuation of the Legacy Minecraft Console Editions(Old Xbox One, PS4, Old Nintendo switch, Xbox 360, PS3, PSVita and WiiU) from 2017 onward.
Answer #1: One significant difference between Minecraft Bedrock and Legacy Xbox One is that while Legacy Xbox One is an abandoned/discontinued version of Minecraft, Minecraft Bedrock is a version of the game that still actively receives updates, and since this version's release in 2017 and Legacy Edition's discontinuation Minecraft Bedrock has about three major feature updates worth of content as this version is currently equivalent to Minecraft Java's 1.15 update, while Legacy Edition is equivalent to Minecraft Java's 1.12 update, so Minecraft Bedrock is where all of the updates are at for the Console Editions.
Answer #2: Minecraft Bedrock is indeed cross-compatatable with others who also play on the Bedrock Engine (Bedrock Xbox One, Bedrock Nintendo Switch, Pocket Edition, and Windows 10 Edition, as well as Bedrock PlayStation 4 soon) when in multiplayer.
This means that people on these versions can play together on the same worlds, servers (this feature is limited to five main Microsoft approved servers for Bedrock Xbox One and Nintendo Switch users, unlike Pocket Edition and Windows 10 Edition users who get more options, but this doesn't effect much from the overall gameplay experience), and realms.
Answer #3: Almost all skins, texturepacks, and DLC packs from the Legacy Console Editions (with few exceptions) can transfer from Legacy Xbox One to Bedrock Xbox One.
One notable thing is that Minecraft Bedrock has their method of selling content a bit different than Legacy Console Editions in the way that while Legacy Console Editions had a shop for skin packs, texturepacks, and DLCs made officially from 4J(the developers of Legacy Console), the Minecraft Bedrock marketplace has a larger variety of content made by both official sources such as Microsoft and 4J, as well as Microsoft-approved unofficial sources such as server managers, content producers, and sometimes fan-made content by regular people.
This content can range from skin packs, to texturepacks, to DLC, to adventure maps, to add-ons(Minecraft Bedrock's primitive version of mods).
However, this Market Place doesn't directly use money to purchase content, but instead they have their own currency (Minecoins) that you have to pay money to get, which in turn can purchase content, so there's an extra step.
Though if I can recall, I think they just recently added the direct payment option to the Market Place if you didn't want to go the Minecoin route however I'll have to check on that again before I could confirm that.