The two on the left are Marthasterias glacialis commonly called the Spiny Starfish. Like many things marine, there can be significant colour variation within the specie. The two colours here are typical of Marthasterias. I think the one on the right is Asterias rubens otherwise caled the Common Starfish. Usually it is a lighter colour - brown/yellow with a touch of red is typical but it is also found in violet as here. It really is a very common beast and can occur in colossal numbers at times.
Jim

I agree this would be Pelagia noctiluca, some times referred to as the mauve stinger. It can give a terrible sting depending on an individual's sensitivity.
You can see a picture of it in my portfolio on this site

Difficult to identify from your description. By far the most common jellyfish you are likely to encounter in this location at this time of year is Pelagia noctiluca. Its colour varies enormously but it is a fairly small and compact jellyfish which fits your description. The question after yours on this forum also relates to this beast - have a look at my answer there for further info.
If the jellyfish you saw had long, fine streaming tentacles, then I am barking up the wrong tree!

Very probably Pelagia noctiluca. A very common small jellyfish with a really painful sting which leaves marks as described. It varies in colour from mauve to brown and the approx. size you give is about right. In the UK, where it seems primarily to be a mauve colour, it is sometimes called "the mauve stinger".
Probably the most common cause of stings while swimming in the Meditteranean. At times can be present in immense numbers leading to the closure of some beaches.
There is a picture in my portfolio on this site.

Difficult to identity from the description. The most common culprit in the Meditteranean is Pelagia noctiluca It can give a tremendous sting depending on your sensitivity. My daughter had a scar on her thigh for 15 years after being stung by one of these. It is very variable in colour but have never seen one with a cross on top. There is a picture of one in my Wild Spain portfolio which may help. It could not be the common jellyfish (auralia aurita) as has been suggested - this does not have tentacles & does not sting
Jim

I think it very unlikely to be a greater weaver - the guide books say that they largely inhabit somewhat deeper water. My own observation support this as I have seen many of them but always deeper than "paddling depth"

Jim Greenfield

Almost certainly a lesser weaver, echiichthys vipera. Up to 15 cms long the fish lies partly buried in sand waiting for passing small fish. The dorsal fin is erected as a defence mechanism e.g. when trodden on!. The fin has four sharp rays - which ties up with the four punctures mentioned - and venom is passed on. This is a relatively common occurence off Atlantic & Med. beaches each year and the pain can be intense. Deaths have been recorded. The recommended treatment is soaking in hot water which removes the toxicity of the venom.

Try the Medas Islands off Estartit - I'm sure you will not be disappointed. Full details in my recently posted article on this site
Jim