Itinerary Help/Suggestions

Generally, itinerary looks good.
I would substitute Ronda for Nerja, and stay just one night, so I could stay two nights in Cordoba (personal preferences for those cities).
Train (or bus) is actually doable for the whole trip from Malaga onwards.. Really good fast trains.
If you particularly want to drive some of the time, there may be a premium for one way drop off, less likely or smaller if you use one of the major companies.
If you have a car, make sure to booking hotels with parking - places can be scarce in these old cities.
Do Northern Spain next time, to do it justice.

You have plenty in this trip, add no more, the trip is rushed as it is.

Hate to be one of "those" people, but you really do not need a car for as long as you have it. Your itinerary really does not allow much time for the actual cities you are staying in, so you will not be leisurely driving the countryside.

A car is probably fine for getting in Malaga, driving to Nerja, then driving to Grenada. It is a toss up whether it is of any advantage for Cordoba, I would be tempted to return in Cordoba, or even Granada.

Between Granada, Cordoba, and Seville are efficient fast trains, use those. You really do not want the hassle of parking in those cities, that would mean staying outside the historical centers, and hotels with parking are limited. If you are going the "AirBnB" route, they rarely have private parking anywhere near the city center. If you want, there is excellent bus service between Malaga and Nerja, and Nerja and Granada. A car might be nice if you wanted to explore some of the White towns or places alomg the coast, but that really is only possible if you were staying in Nerja for a week or so. For what it is worth, I have been to all the places you propose (exception of Valencia), some several times (we will be in Nerja for the third time shortly before you) and have done it all by train and bus. Flying Valencia to Malaga is fine.

Similar with flying from Seville to Madrid, by the time you get to the airport in Seville, through security, fly to Madrid, then travel from the airport into town, you are looking at 4-5 hours of travel/hassle. The train will get you there in three.

I think you are trying to cram in far too much in this plan. For one thing, you have too little time in both Cordoba and, especially, Sevilla. You do not need a car in either of those cities and a car would be an expensive hindrance.

You also have almost no time in Madrid.

I would skip Nerja unless you have a special reason for visiting.

For hotels, what kind of price range?

Here is a vote for a self-drive trip. Driving in Spain is easy and allows for flexibility in terms of timing and route. We have not found it difficult or expensive to park in cities. Would suggest focusing on Valencia (obligatory for you), Seviila, Cordoba, and then Granada. Nerja has nice beaches but is an expat, vs Spanish, community. Malaga is relaxed and lovely if you have the time. The nearby El Caminito del Rey is awesome if, again, time allows. Unless you are a museum buff two days in Madrid is plenty. Segovia is well worth a day. Enjoy!