1. Yes, you can claim half-rate JB while getting OFP. As a matter of interest you can aslo calim FIS and OFP when you are working so that's another example of two SW claims ...three if you include CB!)
2. Regarding rent supplement, each area has a limit on the amount of rent payable that qualifies you for Rent Supplement, whcih is paid by the HSE covering your area. If you are paying rent over the limit reckoned in your area, you will not get Rent Supplement, AFAIK. If you are on the limit or beldow it, you will have to pay the first €13 yourself, again AFAIK.
The length of time in the house does not matter. The Community WElfare Officer (not SW) is the one to go to regarding Rent Supplement.