White Patches on newly painted wall

[Arif Rashed 0]

Hi guys,

Few years back i painted my bedroom wall a dark red color. Immediately white patches begin to show up. I tried wiping them off but it came back shortly after. I didn't use any primer for that paint job. 

Now i am sick and tired of these ugly wall and planning to paint them. After reading thru forums, i believe the root cause is the absence of the primer cause the water from the previous paint job to seep into the new paint. 

My question is, before I prime these walls, do I need to completely remove these white patches first, then prime them or just leave it as it is and paint over them? I am afraid I might make matters worst since i will have to wipe them with water, and prime them after would cause more disaster since the issues is water to begin with. Also I realize that place where my head always lean on the wall when I have hair oil(olive oil) seems to clean of the white patches really well. 

I thought maybe I should wipe my walls with light coat of olive oil and then start with my paint job (primer included this time). Do you think this would cause any problems?

Next what primer do I use? Is water base primers that claim to be have amazing sealant power be sufficient?  or is it a must to use oil- base primers? I read it's a huge hassle to use oil-primes, I really am leaning towards water-base primer because of this.

I am looking at Benjamin Moore paints which are latex base-paints. Can I use a latex-base paint as a top-coat over a water-base under-coat? same goes for oil-base under-coats, is it advisable to use a latex-based top-coat? and have anyone tried using Benjamin Moore paints? which ones do u recommend for our normal HDB wall.

You can see I am truly armature here, I hope anyone who is knowledgeable can shine some light on this. 

I have also attached the photo of my horrific wall. 

[Vodarado 0]

Is this limestone?

[Brandcalfe 2]

I guess there worked a few unprofessional people that doesn't know that the wall should be cleaned firstly, then they can apply the paint. If the wall is not prepared properly, the salt can deposit on it and remain like this. I am not the best in construction, but my friends has the best home improvement company from Australia. He did a lot of things for my house and I am very thankful to him. His guys are real professionals and they can do everything fast and for a very good price!