Being on a date or being in a relationship? It's the latter in Polish. Learning Spanish is really superbly easy if you know Polish.
Doubt it would be the same the other way around, hi hi.
Ir would also be possible if you're talking about actually going somewhere:
- Voy a la tienda ¿Quieres ir conmigo? - I am going to the store. Do you want to go/come with me?
But "caminar con alguien" also translates as "to go with someone", in the meaning of "dating someone".