Three questions...please help if you can!

1. We have estimates for a sealed internal French drains vs. one with a small (less than an inch) gap in the drain. If a water problem occurs from i.e. a broken water pump from the washing machine, will either of the above let the water on the floor into the French drain system?

2. What is a mira drain? Can the use of a mira drain (dimple board) be related to the above question?

3. We are having the concrete walls smoothed (from spalling)and then patched with hydraulic cememt. We are then having the walls painted with a waterproof paint. The floor will be painted with 3 coats (one contractor) or cosmetically (another contractor by our request). There are no cracks on the floor. We have some cracks in the wall but water does not seem to have come in from them. Are there any brands of paint or hydraulio cement that are poor performers and should be avoided? No one is using Dry Lock.

We are very confused. Any help would be greatly appreciated. Thank you!