1. You are right. If you have been back at work for 8 weeks you are no longer in the same period of incapacity for work, & SSP entitlement starts again.
2. Your employer must either pay you or give you an SSP1 form explaining why they think you are not entitled to SSP. If necessary, you should then dispute it with them.
3. I don't understand why you could not get ESA. Assuming you have been working & paying NI for a sufficient period (rules are a bit complex) you should have been entitled to contribution based ESA, which is not means tested. Do look into this as, if your employer refuses to pay you SSP you can use the SSP1 to claim ESA.