In summer 2008, myself and family stayed in the Natura palace, which is a lovely hotel, an absolutely faultless 4* + Thomson Platinum, couldn't recommend it more if you're looking for a lovely relaxing holiday in Lanzarote! However, unsure as to if this fits your budget because it was 2 years ago we stayed there and it was in peak summer holidays (July / August), and I recall it being around £800 pp on a half board basis for 2 weeks, including flights. However, prices will be different for the time you will be going.

Anyway,

1. The weather should be lovely early July, I know when we went late July & early August, it was at least 30 degrees most days. Also, there is a wind but this is a warm wind and not so bad it will blow sand in your eyes!

2. Can't comment on the mentioned apartments, but I think you will need air conditioning at night, it is very hot!

3. Again, I don't know about the building works or that part, but I know there was a man made beach in playa blanca that was good and was SAND, not rocks like most of Lanzarote seemed to be.

4. I think it depends on what deals you can get as package holidays now or if you want to take the risk for a cheaper deal nearer the time.

I hope that helps!

Hi
We stayed in the Sun Park a couple of times but it is quite a few years ago. I do know a young couple that went last year and they really liked it. They are in quite a good location, about 10 min walk from the centre of town and 5 mins from the Dorada Beach and close to a Hiperdino supermarket. The Sun Royal is just a bit further on up the road. Not sure about the aircon but we have been to Playa Blanca many times July/August and never had any and it was never an issue. The Sun Park was closed for a few weeks recently for some improvement work to be done.

The Dorada beach is the best beach IMO. Sunbeds, parasols, beach bars and watersports. I doubt the Flamingo beach will be open by then but if you do stay in either of the accommodations you mentioned the Dorada beach is much closer. The Flamingo was a nice beach but it didn't used to have the facilities. There is also a small beach in town.
The weather should be really good and any breeze will be very welcome. We have only been a couple of times in July when the wind was a bit on the strong side, but nothing too bad.
The Papagayo beaches are really good and you can reach those by water taxi from the harbour. All the resorts beaches are white sand. You will find some black sand beaches if you go out and about.
You might find this helpful.
http://www.hotelstreet.co.uk/Map-223-Playa_Blanca.html. It shows the location of hotels/apartments.
The Dorada beach is infront of the Princesa Yaiza hotel.