does this element form oxides as well?
Yes - Dichlorine monoxide, Chlorine dioxide
Chlorine
Dichlorine monoxide (ClO) is a brownish-yellow gas (red-brown when solid or liquid) which may be obtained by reacting chlorine gas with yellow mercury(II) oxide. It is very soluble in water, in which it is in equilibrium with hypochlorous acid (HOCl), of which it is the anhydride. It is thus an effective bleach and is mostly used to make hypochlorites. It explodes on heating or sparking or in the presence of ammonia gas.

Chlorine dioxide (ClO) was the first chlorine oxide to be discovered in 1811 by Humphry Davy. It is a yellow paramagnetic gas (deep-red as a solid or liquid), as expected from its having an odd number of electrons: it is stable towards dimerisation due to the delocalisation of the unpaired electron.
is chlorine bleach a pure substance or mixture Calcium hypochlorite is an inorganic compound with formula Ca(ClO). It is the main active ingredient of commercial products called bleaching powder
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Chlorine [SEP] Chlorine oxides
The chlorine oxides are well-studied in spite of their instability (all of them are endothermic compounds). They are important because they are produced when chlorofluorocarbons undergo photolysis in the upper atmosphere and cause the destruction of the ozone layer. None of them can be made from directly reacting the elements. Dichlorine monoxide (ClO) is a brownish-yellow gas (red-brown when solid or liquid) which may be obtained by reacting chlorine gas with yellow mercury(II) oxide. It is very soluble in water, in which it is in equilibrium with hypochlorous acid (HOCl), of which it is the anhydride. It is thus an effective bleach and is mostly used to make hypochlorites.