1. We have two DCF (Zpacks Duplex) and one silnylon (Big Agnes Tiger Wall) tents. DCF is more waterproof than silnylon (perhaps by a factor of 10). Yet, under heavy downpour, a DCF tent can be "misting" -- water pressure lets a fine mist through the fabric, and occasionally a drop of water. This said, we were caught in a major rainstorm this past summer and our Tiger Wall was still reasonably dry. So... if things got damp under your tarp, probably normal. If you mean that you could see small pools of water, probably not normal.
2. You can recoat. Search should return several recipes, including spraying silicone (available at most outdoors stores, meant for tents and rain gear). Should improve things, but I'd say -- do not expect perfection. In particular, my experience with rain jackets is that these treatments do not last for long.
3. Depending on your circumstances, you may want to consider a DCF tarp. Our DCF tents are still in decent shape, after hundreds of nights over the past 7 years.