There's no direct connection between Margaret bridge/island (Margit híd and Margit sziget) and Vajdahunyad castle (Vajdahunyad vára), but I'm trying to put multiple parts of the Hungarian capital Budapest in one post, so I just make 'em connect :-)
Margaret bridge is one of eight bridges connecting the two parts of the city, Buda and Pest. It's a special case however, since it actually connects three pieces of land: Margaret Island, in the middle of the Danube, is accessible via the bridge too. The same connection is by the way made on the northern tip of the island by Árpád híd, the difference being that the connection to the island was originally provided in the design of Árpád bridge (built in 1939), while it was only added later on in the design of Marget híd (built between 1872 and 1876, with the connection to the island only realised in 1899).
You can read all about Margaret bridge here. For ample information on the Holy Crown and the crooked cross on top of it (#2) I'll have to refer to the Wikipedia-article on the subject. There's more theories on the cross, but the article as a whole is not bad, especially since it does not forget to mention the holiness doctrine (the crown is more important than the one wearing it). As for the view in #3, the Hungarian national parliament (országház), I'm pretty sure you must have seen it before (it's definitely one of the worldwide best known buildings in Hungary). You can read more about the building here (and a visit is definitely worth doing, though you should make reservations in advance).
As for Margaret island: it is not as well known as Óbuda island (where every year in August the Sziget festival is held, one of the largest music and cultural festivals in Europe, with more than 1,000 performances and nearly 500,000 visitors), but it's way more interesting, and during the year (when there's no Sziget festival) it's definitely more popular. Apart from the romantic walkways (the island is 2,5 kilometers long), it contains medieval ruins, a rose garden, two musical fountains (which attract a lot of tourists, especially children), a historic water tower, swimming pools, playgrounds, water parks, an open air theatre and cinema, a number of clubs, and ... a small zoo. That's where I "shot" the stork in #1.
And then Vajdahunyad castle (Vajdahunyad vára). It's, as mentioned in an earlier post, part of the Városliget park, and was - just like Heroes square (see this post) - constructed in 1896 for the Millennium celebrations. It's thus a "fantasy pastiche", not a "real" castle, showing the Hungarian architectural evolution through centuries and styles. It's Romanesque, Gothic Renaissance and Baroque all at once. For the Millennium celebrations it was actually build of ... cardboard and wood, but it became so popular that it was rebuild in stone between 1904 and 1908.
Among the statues the most famous one is that of Anonymus. He is the - anonymous - person, a notary of king Béla III, that wrote the chronicle Gesta Hungarorum (Deeds of the Hungarians) in the beginning of the 13th century. It is the first written Hungarian history and deals principally with the Hungarian (Scythian) conquest of the Carpathian Basin at the turn of the 9th and 10th centuries. (Full translation to English: here)
A statue which I don't have in this post is at the castle too: it's the one of Béla Lugosi, the Hungarian born American actor (his full name is Béla Ferenc Dezső Blaskó and he was born in Lugos - hence Lugosi, meaning from Lugos - nowadays part of Romania) most famous for his role as Count Dracula in the classic 1931 film Dracula by Universal Pictures.
As always: I do not repost all my previous Flickr photos to Photoblog, but ... I have all my photos on another medium too: Pinterest. You'll find all my Budapest 2015-pictures here.