OP, unless your DF is a landlord with a track record of letting properties, it's very unlikely that you will be satisfy the DWP that this is a "genuine commercial arrangement" and they are highly likely to refuse to cover the rent. Imo, the purchase of a property for you to rent is almost certain to be considered a "contrived tenancy" and they will then refuse to pay.
If he's already a BTL landlord, you have a chance, but I'd still give it a 50/50 chance of succeeding, at best. They could well consider the recent purchase of a property as an indication that your tenancy is a contrived one, despite him being in the renting game. My advice (benefits adviser) would be to look for a private rent elsewhere.
With regard to timing your claim, the "monthly assessment period" (MAP) will start on the day you make your claim, and end one month later. Someone starting a claim today will have a MAP that starts on the 7th of the month and ends on the 6th of March, and this pattern will apply for the duration of the claim.
This is where you need to be canny with tenancy start dates. They don't pro rata, so if, using the example above, you had a tenancy start date of 4th March, you would be entitled to housing costs for the whole of the MAP, even though you had no liability to pay rent for most of it.
And you can't start a claim until you actually move out, until that time you will be treated as a couple and any claim will be a joint one, with your husband's income taken into account.
Ideally, you don't want your MAP to start/finish close to your pay date if you are in work and paid monthly, for the reason PPs have mentioned.
If you get an advance payment, it will be repaid over 12 months and you need to factor this in to your budgetting.
If, by any chance, you get the daily living element of PIP, you won't go onto UC at all, but will have to claim under the old system (housing benefit, tax credits and JSA/ESA or income support), but the "contrived tenancy" thing will still be an issue.
It would be far, far better if your "D"H moved out. It would simplify things no end.
Good luck.