Who fills 10 million vacancies ? Where will 10 million "Britsh" cars come from ? Most criminals are not kids. There is housing shortage and most needing homes are under 50. £100 week for booze and fags sounds good; Can we legalise weed and add that please.
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First, you propose an instant spend of £10,000,000,000,000—that is ten trillion pounds. Where is all of that going to come from?
Second, as many others have pointed out, paying off mortgages for people already in homes isn't going to create homes for people who don't have them.
Next, if you want to instantly remove all the older people from their jobs, where will be the expertise to train all those coming in to replace them, and who will pay for the massive recruitment costs the companies will be saddled with?
There are many, many things wrong with your proposal to put people needing care into prisons. Just a selection of reasons are that prison life is not the luxury you think it is, prisoners do not have individual rooms, being locked away for 18+hours won't do for those needing care, the prison officers are not employed in numbers equal to care staff, 20 minute check-ins only occur for small numbers of people on suicide watch, medical care and medicines are only provided for a minority rather than every inmate, and your proposal to leave rapists unsupervised in a care home will result in them absconding.
The logic you've reproduced from a chain letter/email you received doesn't really stand up to any level of scrutiny.