1. I believe the nominative form is "Vodičkova ulice". Is that correct?
2. The word "ulice" is feminine singular. Correct?
3. What kind of word is "Vodičkova"? Is it a noun or an adjective?
4. Does the word mean anything? Is it the name of a person?
5. Suppose I want to say "on Vodičkova Street", using the preposition "ve". What case follows "ve"? Is it locative?
6. How do I modify the words after "ve"? Is it "ve Vodičkově ulici"?
7. Instead of "ve", can I also use "na"? What is the new phrase with "na"?
4. It is called after the name of the historian of czech literature Felix Vodička
The word 'Vodičkova' means 'of Vodička' or 'Vodička's'. I don't speak Czech so I'm not sure if they treat it as adjective or noun in Genitive case (like it would be in Polish: 'ulica Vodiczki').
Nobody answered until now, so I decided to write my guess and I hope native speakers will answer you soon.
There are different rules for soft adjectives, hard adjectives and posssesive adjectives.
Vodičkova ulice: Vodičkova = possessive adjective
ve Vodičkově ulici
Dlouhá ulice: Dlouhá
= hard adjective
v Dlouhé ulici