@Abdul Azeez I'm a little late to this party but I'll provide some background on your issue from a contractor's perspective. Thanks for the great videos and pictures. I wish more people would post like this when they have issues.
First of all, one of my biggest pet peeves is people stating that "basements should never be finished" or "you'll never dry out a basement". That's a bunch of garbage coming from people who don't understand the science behind construction and building design. Basements can be finished just as well as any other part of your home and should be enjoyed as such. People who "fix" their basement water problems and still have issues haven't fixed the core issue. Basement water issues aren't some mystical creature that requires voodoo or black magic to cure.
- Efflorescence is the byproduct of water intrusion. It's a salt that's left on the surface of the block due to water being sucked through the building material. What most people fail to realize is that brick, block, wood, etc is porous. It's made up of small capillaries which wick water from the outside and push it throughout the block. This wicking action causes pressure (hydrostatic pressure) which forces the water and salt out at the path of least resistance. This can often result in damage to the block known as "spalling" (Where chunks of the face of the block have crumbled away). While the efflorescence is a cosmetic issue, spalling would be of more concern.
-I think all of the above posters, as well as yourself, have nailed the easy solutions. Gutters cleaned and maintained, extended downspouts, proper grading away from the house (anywhere from 6" over 10' to an inch per foot depending on where you read. The point is the grade should extend far enough out from the house to prevent water from findings it's way back to the foundation).
-French drains/sump pumps are the go to solution for many companies because, while labor intensive, they solve 99.9% of basement water issues inside the home. It doesn't generally fix the problem of intrusion but diverts the water at the wall/floor joint to prevent your floor from becoming wet. This is a perfectly acceptable solution and when installed properly works very well. I have had three of these installed without issues on sale, inspection, or complaint.
-The ultimate solution is the installation of a capillary membrane. In older construction, this would have been the painted on tar below grade on the exterior of the foundation. The new material consists of a rubber or plastic membrane which prevents water from being wicked up by the block. At this point, it doesn't matter where the water goes around the foundation because the membrane is impermeable. This is the most expensive option requiring a trench to be dug around the exterior of the house several feet deep. I don't believe that you need that in your case as it doesn't look like you have an extreme amount of intrusion.
-I would be interested in seeing whether or not you have a French drain currently installed in you basement as the cut against the wall leads me to believe that you may. The other question would be where does the water collect if there isn't a sump pump?
-You can paint the walls with DryLock or some other paint but it really doesn't solve your problem in any permanent fashion. Eventually, the hydrostatic pressure will bubble and crack the paint (as it appears it already has) and you'll be back to where you started.
-Correct some of the easy things like you have and see if your problem slows or is rectified.
-After your moisture issue is corrected, have your contractor install plastic moisture barrier, followed by your stud wall with a 1" stand off distance to prevent moisture accumulation. Drywall and finish as normal.
Don't let a wet basement scare you off. There are plenty of solutions which won't break the bank. I would suggest getting opinions from several basement contractors and landscapers. Landscapers can advise you on proper grade and drainage without the sales tactics of pushing a particular basement system. Good luck and let us know how it turns out.
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