Quote Originally Posted by Gottimhimmel View Post
Надеяться means "to hope, expect"
My question is, do you use the dative or nominative!
Nominative.
"Я надеюсь".


Quote Originally Posted by Gottimhimmel View Post
and in a further point, when do you use the dative, such as "мне холодно, мне нравится"
Are there rules behind it!?
1. Dative instead of nominative is used with a wide range of adverbs such as холодно, жарко, смешно, грустно etc. These adverbs are named категория состояния.
"мне холодно" literally means "for me, [it is] cold".
Actually, категория состояния can be used not only with dative. Other constructions exist too. For example:
"У меня на душе спокойно" - "In my soul, [it is] quiet/peace".

2. There are some verbs such as хотеться, спаться and so on. They should always be used with dative. For example, "мне не спится" = "for me, [it] does not sleep" = "I cannot sleep"; "мне хочется гулять" = "for me, [it] wants to go for a walk" = "I want to go for a walk".
There is no way to determine if a verb ending with -ся is a "normal" verb or a verb requiring dative. So you have to remember them.
Fortunately, these verbs are very rare, and in most cases "normal" verbs can be used instead of them. For example:
"мне хочется гулять" = "я хочу гулять"
"мне не спится" = "я не могу уснуть"

3. "мне нравится" is a different case. The verb нравиться is a normal verb in the grammatical sence, but its lexical meaning is a bit weird. It can be explained as "similar to English verb to like, but in passive voice".
In English, we can say "I like her", so "I" is a grammatical subject and "her" is a grammatical object. But in Russian, the verb "нравиться" requires us to use "her" as a subject. So we should say "Она мне нравится". Literally, "She is-liked for me".
It looks strange, but that it is.


Quote Originally Posted by Gottimhimmel View Post
And when does one use just "мне нравец" instead of the -ся
нравец is not a word. That is wrong.