Applying for Tier 1 and claiming benefits in the past

[wp-spouse]

Hello All,
We are planning to apply TIER 1 (G) in Oct 09. Right now we are in WP since Oct 06. During this period, due to some incorrect understanding, we got 10% reduction (2nd home reduction)in Council Tax by showing that we have a house in India. Also after the birth of our child we claimed Child tax benefit for 3 months. In both the cases, the moment we realised that we are not eligible, we voluntarily informed this and stopped the reduction/ payment.
Now my question are:

a) While filling up the application form do we need to specify these two cases?
b) Will HO have knowledge of this?
c) Can they deny our application based on these incidents?

d ) Edited to Add: Will the 10% Council Tax Reduction of 2nd home be considered as Benefits? If no then do we need to mention this in the form?
e) If we return back the Child Benefit money before applying the Tier 1,even then do we need to mention everything in the application?
Need some expert guidance on the same.

Many thanks in advance.