I doubt hot cross buns are a vestige of Anglo-Saxon/Germanic paganism. The hot cross bun in England is recorded in the 14th century, Alban Buns – more or less like modern ones I believe – were distributed by the monks in St Albans to the poor on Good Friday. Where this tradition came from or whether it was invented there and then is open to debate, however, the Byzantine Greeks had been making buns or cakes marked with crosses as early as the 6th century CE. I’d be interested to see a historical source to support the idea that hot cross buns were used by the pre-Christian Anglo-Saxons.
Ēostre is highly problematical in terms of defining ancient belief(s). We only have one certain reference to her, and that is thanks to the Venerable Bede writing in the 8th century CE. There’s nothing elsewhere, other than a tenuous link to a dwarf (male) in Norse writings. It’s not until the 18th century that Grimm attempted to find some vestiges of Ēostre in Germanic folklore, and he did not really come up with anything that could really confirm much. It is to Grimm that we owe the association of hares/rabbits with Ēostre, however, there is no historical evidence to back up this claim. In fact, it’s just as likely that the hare emerged as part of Medieval Christian belief – for some reason, hares were believed to reproduce asexually and thus were associated with the Virgin Mary and the birth of Christ. As odd as it may seem to us today, people had some pretty strange ideas about natural history and biology in the past. As for the eggs, it has been suggested that they originated in Christian communities in Persia/Iran and spread through the Greek/Russian Orthodox communities until reaching the Catholic and, later, Protestant communities in Western Europe (see: Kenneth Thompson, 2013). Others have theorised that the eggs may be connected to Lenten practices when giving up meat, fasting on other personal sacrifices were mandatory.
Linguistics would trace the origin of Easter>Ēostre to an Indo-European word meaning “dawn”, so what Bede may have recorded could have been: (1) the exact historical existence of an Anglo-Saxon goddess Ēostre; (2) a celebration connected somehow with dawn or a deity of dawn; (3) something else half-remembered; (4) something he made up. Of course, this raises another question, i.e. how much we can rely on Bede. I’d take anything written by ancient historians with a healthy pinch of salt, that is not to say they weren’t on to something either.
Interestingly enough, however, we have Tacitus’s account of Boudicca divining with a hare and honouring Andraste – if we can rely on Tacitus, too, and we have a Gaulish river goddess by the name of Abnoba from the Rhineland area who is depicted on a statue with a hare. The amount of folklore associations with magical hares are too many to number, but as ever, it’s difficult to separate what may have been ancient pre-Christian belief from Medieval Christian superstition and folklore.