And you will have to google/youtube the story either way, at your own pace. As a f2p you get the New Light quest, some strikes, 1 dungeon, and 2 raids. The free to play version of the game is a demo at best. There's no limitation on power level or anything like that, but your available content is very limited. It is 1800, 1000, 500 for very high, high and medium. The price is for the server you are moving to. It is absolutely possible as other folks have said here. My only caution is the lag can get really bad depending on where your friend is located. I'm in NA and played on EU (still do every few months) for a year.
Plus most core builds are significantly disadavantaged vs HoT or PoF builds. And the matchmaker only looks for the classes and not which specs those classes have equipped. So it can happen that your team has 2 vanilla guardians and enemy team has 2 dh or firebrands. Or 2 scourge on one side and 2 vanilla necroes on other side. Seen it all.

No free item appearing when I log into an old paid Core account. Not on F2P Steam account either. Or is there some per-IP limit on the gemstore promotion?

This would open a huge can of worms where people could easily unlock all the mount skins for free. The free giveaway is a fun way to celebrate 10 years of guild wars 2 and give a little back to the community the helped Anet get this far. Its a mount skin so its not really that little but you get the point. Multiplayer is fully free and has all the units. The only thing locked is you have to get 10 first wins of the day to play ranked, but you can play unranked at that time (which is literally the same ladder, just without league badges), and you can bypass it if you own any of the non-free campaigns. Heart of the Swarm, Legacy of the Void and bceq. 154 78 17 192 158 194 186 310 73

guild wars 2 f2p vs paid