What are these symbols?

Question

1. ゐ and ゑ. Looks like an odd looking hiragana, but i never seen it before in the hiragana list.
2. ゝandゞ. What does it mean, and why there is a dakuten in the second one.
3. ヶ. It looks like ケ. Maybe it is ケ. I only know that it is readed か or が. Example: 藤ヶ谷 (ふじがや).

― 檜原 クリスチャン

Answer 1

In modern あいうえお, the column of わ is わいうえを, but it used to be わゐうゑを. The pronunciation of these were more like "we" and "way" as opposed to the normal い and え sound. I didn't know this myself, but apparently these old forms have disappeared as recent as 1946.

ゝ is a short-hand that means "repeating the previous letter", such as 学問のすゝめ (学問のすすめ). As you probably know, dakuten is composable decoration of a letter, and it can also decorate ゝ.

ヶ is an interesting one. I think its origin is at least in part katakana ケ, but I can't think of other katakanas that do this. Aside from the usage in 藤ヶ谷, which means 藤の丘, you also use ヶ to count objects, like 10ヶ.