customs and immigration – UK visit visa refusal based on Finances

I was recently refused a UK Standard visit visa For two reasons. the online application I answered the question do You have any income or savings? No!(Mistake no1) because I Had also stated I have £100 monthly exPenditure, of which what I meant was I get £100 In cash from my Mother for personal use.So the case worker siteD how I spend that if I have no income or savings.
So how do I rectify this in my re-application? On the income and saving do I state the £100 and explain in the cover letter who I get it from and it’s use?

2.I provided my bank statement with £2000. The money was withdrawn from my mother’s personal account and I then deposited the funds into mine. However when my mother requested for her bank statements, we don’t not thoroughly check them and it turned out that the dates on which the withdraws were made had been missing as the Banks statements given were just other random transactions(mistake no2). And so the origin of the funds came into question.

How best can I correct this in my re-application?

I figured, if I provide the correct and precise Bank statements that will show the amounts and date of the with draws, which will coincide with the amounts and dates of deposits made into mine, that would clarify the issue.

However am here to seek advise and any effective alternatives would be helpful. Thank you