Hi there Para Chen! Let me start with “just over there”. This phrase is used to indicate something close to the speaker. This sentence refers to a side path, which is connected to a main path (or a main road). The sentence tells us that the side path moves off (or branches off) to the right of the main path. Hope this helps.

In this context, "towards" means "in the direction of" or "nearly at". So there is a side road which goes to the bank, and the parking spaces will be on that road, near the bank (or at least, nearer the bank that where the person is standing now). "Up" could be an unnecessary word. It's is POSSIBLE that the road goes uphill. However, it might not! e.g. people often say "I'm going up to London" when there is no uphill. To make things more complicated, people also say "down" e.g. "I'm going down to London" or "let's go down the pub" (this one is very British). I cannot explain why we do this, we just do. All your sentences are very informal, chatty English. The meanings are often not precise.

New parking spaces on the side road up towards the bank. Please, can you tell me that waht the meaning of "up towrds"?

Wow. Your describtion is very vivid, thank you, I have understood that .

It is describing the path like the branch of a tree. It splits from one into two like a tree branch. 'Branch off to the right' means the split of the right side (not the left).