Chemistry:difficulty in understanding these statements:-

[leena19]

'As the atomic radius increases down Group 7 halogens,the ability to accept an electron decreases,(this, I understand).
As a result,the reactivity of halogens decreases down the group and also the oxidising power/ability of the halogens decreases down the group"

It is the part in bold that I can't understand.Does the oxidising power stated here refer to the elements' ability to act as oxidising agents?Atleast this is what I think, considering the Cl2 water test,but elsewhere ,my notes on the periodic trends state that across a period 'the reducing power/reducing ability infact,increases across a period'.
Now I'm confused,'cos if the first were true,that would mean the ability to undergo oxidation would increase across a period which seems a bit absurd,I think?

My other problem is, "down the electrochemical series the higher metals replace the lower ones,but for the non-metals in the series the reverse is true,the nonmetal lower down displaces the one higher",but how so,I tried googling but I didn't get a comprehensive answer.

Hope my problem is clear and I really hope someone can help me understand .
THANX IN ADVANCE

[chemisttree]

The normal oxidation state for a halogen is -1... thus, the neutral atom must grab an electron from somewhere to achieve that electronic configuration.

What is the definition of oxidation?

[leena19]

Oxidation is when an atom,
1. gains oxygen
2.loses electrons
3.loses protons ? Thus the oxidation no. of the atom increases

[chemisttree]

When something oxidizes something else, it grabs electrons. The thing that supplied the electrons is oxidized and the thing that did the grabbing is reduced.

[leena19]

When something oxidizes something else, it grabs electrons. The thing that supplied the electrons is oxidized and the thing that did the grabbing is reduced.

Yes.I understand this.the thing that oxidises something else is an oxidising agent and that which underwent oxidation is a reducing agent.

But what I don't understand is,
the reactivity of halogens decreases down the group and also the oxidising power/ability of the halogens decreases down the group"

the meaning of the phrase 'oxidising ability/power' as used here.I think it means the elements' ability to act as an oxidising agent cause I believe Cl2 is a better oxidising agent than Br2,I2, which is the basis of the Cl2 water test,right? so...their ability to act as oxidisnig agents decreases down the group?
But if my interpretation of "oxidising ability/power' were true,
my notes on the periodic trends state that across a period 'the reducing power/reducing ability infact,increases across a period'.

how can this also be true?
This would mean that across a period ,the ability to undergo oxidation increases across a period?
I'm extremely confused.
Need some help here,please...