I can answer the first one for you. It will take some time to process your OFP claim, but if it's approved, you will be entitled to payment from the date you applied.
If you're available for and seeking full-time work, you may be entitled to Jobseeker's Benefit based on your PRSI contributions. You can claim Jobseeker's while you're waiting on your OFP claim to be processed, and you might be entitled to part of your jobseeker's after your OFP claim is decided.