Do I need to redo this deck or it would be OK to clean it and repaint it?
Yes, your deck is a bit tired. I don't think anybody can tell you whether to re-do or re-hab without seeing it, but these are the sorts of things I think about on a job like this:

Safety: are any boards going to break any time soon? Are they excessively rotted? Can they support an adult bouncing on them? Do you walk around in bare feet, and are slivers a concern? (I see bits that might catch.) Are the stair treads (and whatever holds them to the stringer/carriage) solid? It looks like one has been replaced already. Are the nails popping up in a way that's going to trip/injure people? If so, those could be pulled and replaced with screws.

Aesthetics: do you care about cracks, or is that okay from a wabi-sabi perspective?

Doing a thorough re-decking is almost as hard as building a deck from nothing, so don't sign up for this task without being ready for work.

On the other hand, a good pressure washing and coat of stain is relatively easy and might yield just the result you want.

Dunno. But good luck deciding.