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It is impossible to say if the repair is permanent, since we can't duplicate the conditions that caused the original leak. Under the right conditions, any basement will leak, so there is no definitive answer to your first question. The fact that you can't look at the repair is not ideal, but is common in finished basements where the owners want to get on with their enjoyment of the room. You could hardly expect them to leave the repaired wall open forever, or to cut open the wall for you unless you have committed to buy the house first.
Exterior waterproofing or the installation of a drainage system at the base of the foundation walls is the most thorough repair for a recurring water problem, but it may be an overly extreme solution if the original leak was caused by a special circumstance, such as a broken or overflowing gutter or unusually heavy rainfall. Perhaps you should try to find out from the seller how, when, and why the leak occurred. The hole or crack in the wall may have been there for years, only causing a problem under the "unusual" circumstance!
The cement slab you mention could be a part of the problem if it is not sloped away from the foundation. If there is a slope away, even a slight slope, the slab should keep the foundation dryer by directing water away from it. An acceptable slope for a new slab near an existing structure is approximately one inch of slope for every ten feet of slab. A slab can be raised to increase the slope, it can be coated with new cement to the same effect, or broken apart and redone. It really depends on how large the slab is and how much work you want to get involved it!
I have done countless small crack repairs with various cement patching products. If done properly, these repairs can last as long as the wall itself... long enough to be considered permanent. If you decide that you want to open the wall to inspect the patch, you might want to add a waterproofing coating (not a sealer) over the repaired area before closing the wall. Think of it as a cloth diaper over a Pamper... backups are always a joy!
Oh, and be sure to choose a waterproofing product designed to be used below grade.
Your common senses are correct... eliminate the obvious first. Be sure that your gutters (if any) are collecting the roof water and directing it away from the house. The poorly graded walk is an obvious suspect, and should be repaired.
If the source of the problem water is beneath the ground, neither of these solutions will fully solve the problem. Movement of ground water can be opposite the apparent grade in some circumstances. "The Original Basement Waterproofing Handbook", is perhaps the single best-ever book on basement waterproofing. If your "above" ground solutions do not yield you the results you desire, this book is a must read! After all, knowledge is power.
As I know you know now, from experience, efflorescence is a mineral deposit caused by the migration of mineral-rich water through your basement walls. In new concrete work, efflorescence can be a short-term problem that may disappear over time as the new walls dry out. However, if this is a long-term problem there are two possible ways to eliminate it.
Removing all traces of the efflorescence by scrubbing and cleaning with muriatic acid (most dangerous) or phosphoric acid (less dangerous), drying the walls (they do not have to be totally moisture free... just not wet) and applying a quality below-grade cement-based waterproofing paint will definitely diminish and may even eliminate the problem. Be warned... if other sealers or paint products have been applied to the walls, there is the possibility that the waterproofing paint will not adhere and the results may be disappointing.
You need to keep in mind that these waterproofing products are not designed to stop flowing water. Actual leaks must be stopped either by sealing them inside with a concrete patching compound (with a high risk of eventual failure) or doing some more labor-intensive work outside your home. The solution could be as easy as cleaning your gutters. Then again, it could require diverting the water through regrading (if the source is surface water) or even installing a drain system at the base of your foundation. A professional evaluation might be advisable so you can assess all your options. Perhaps the best book on this topic is "The Original Basement Waterproofing Handbook" by Jack Masters. You will know as much about your foundation and ground water movement as many of the waterproofing contractors you will speak to!
Once you have eliminated most of the moisture moving through the walls, then and only then can you install your vapor barrier and walls. Yes... even after the waterproofing steps you must still install a vapor barrier because there will still be some low level of moisture movement through the walls. You don't have to worry about mildew… the vapor barrier will form a "stabilizing zone" that will not promote mildew growth… there is nothing for the mildew to feed on!
On the subject of basement walls, there are a few basement wall systems that are both time and labor saving alternatives to standard 2x4 framing. One is offered by Owens Corning and features wall panels with insulation and channels to run electrical, telephone and cable TV wiring. Check it out at http://franchising.owenscorning.com/bfs/.
Dow Chemical offers a somewhat different system, using specially slotted 2'x8' Styrofoam panels that can accommodate a 1"x3" nailer... suitable for the installation of wallboard. Using "green" water-resistant wallboard... at least for the bottom half of the walls... would be advisable. The one drawback to this system is that all your electrical wiring must be on the surface... visit your local home store for the scoop on surface wiring systems. Ain't competition grand!
Don't throw away your dehumidifier. Any below grade area that is anything less than swimming-pool-sealed will have some moisture leaks... especially in the warmer months... and a dehumidifier will keep the air moisture level acceptably low. Again, and I can't reiterate this enough, you are doing this to protect your property and your investment in what will be a wonderful renovation!
If you don't take these extra steps you will regret it. I have seen too many basement renovations that did not take into account the damaging effects of moisture and I have taken roomfuls of once-nice furniture to the dump because of permanent mildew damage. You have to be proactive so that you not only keep the value of your home but increase it through wise use of your hard-earned money!
Any breach through a below-grade wall has the potential for leakage. This includes water pipes, electrical wiring and holes from the metal ties that held the concrete forms together during the pouring of the foundation.
There are a number of products that are designed to stop leaks in concrete walls, the best from a do-it-yourself perspective being hydraulic cement... a.k.a. "Water Plug". This Portland cement product sets quickly and expands while drying. It sticks tenaciously to new or old concrete and will provide an excellent water seal between metal pipe and concrete... provided the metal is not too dirty!
Hydraulic cement needs at least an inch or two of "depth" and a half inch of width in order for the cement to have sufficient and reliable holding strength. Carefully chisel or drill out (with a masonry bit, of course) an adequate width and depth of concrete surrounding the pipe. Rinse off any dust or dirt and, while the wall is damp, apply the hydraulic cement with a metal or wooden tool, packing it tightly around the pipe. You can smooth the patch with a damp tool but work fast, since you will only have a minute or two before the initial hardening occurs. Once the patch hardens, your leak should be permanently stopped. The ground water will still be there, of course, but it will find its way to your drainage system instead of your basement floor!
I would not use marine epoxy in this specific instance. Expanding foam may or may not work in this instance, again due to the depth of the cavity to be filled. Not that there isn't a place for expanding polyurethane foam in sealing leaks in concrete walls. For example, it is one of the few sure and easy solutions for leakage through a pipe containing electrical wiring, such as from a well pump or underground wiring for light posts. The foam will not damage the wiring and will expand to fill every nook and cranny in the pipe!
And forget Goop! Though dry Goop is waterproof, it is not designed to stop leaks, especially under pressure.