After reading the contents I am in view that you have no any structural drawing. If you have structural design then there would be RCC COLUMN for taking the load and wallto be designed with RCC Wall with brick wall.
Now as stated by you that you are using sub standard bricks, change the sub standard bricks emmidately and also do water froofing in the basement.at gharexpert website there is section of basement you should find lot of material for basement construction. Link is given below
Do cement coarse sand plaster 1;3 on both side of wall to strenten the wall.